Transmission method, reception method, transmitter, and receiver

ABSTRACT

In a transmission method according to one aspect of the present disclosure, a encoder performs error correction coding on an information bit string to generate a code word. A mapper modulates a first bit string in which the number of bits is the predetermined integral multiple of (X+Y) in the code word using a first scheme, the first scheme being a set of a modulation scheme in which an X-bit bit string is mapped to generate a first complex signal and a modulation scheme in which a Y-bit bit string is mapped to generate a second complex signal, and modulates a second bit string in which the first bit string is removed from the code word using a second scheme different from the first scheme.

BACKGROUND 1. Technical Field

The present disclosure relates to a transmission method and a receptionmethod with a transmitter and a receiver, in which a multi-antenna isused.

2. Description of the Related Art

Conventionally, for example, there is a communication method called MIMO(Multiple-Input Multiple-Output) as a communication method in which amulti-antenna is used.

In the multi-antenna communication typified by MIMO, at least one seriesof transmitted data is modulated, and modulated signals aresimultaneously transmitted at an identical frequency (common frequency)from different antennas, which allows enhancement of data receptionquality and/or data communication rate (per unit time).

FIG. 72 is a view illustrating an outline of a spatial multiplex MIMOscheme. In the MIMO scheme of FIG. 72 , configuration examples of atransmitter and a receiver are illustrated for two transmitting antennas(TX1 and TX2), two receiving antennas (RX1 and RX2), and two transmittedmodulated signals (transmission streams).

The transmitter includes a signal generator and a radio processor. Thesignal generator performs communication path coding of the data toperform MIMO precoding processing, and generates two transmitted signalsz1(t) and z2(t) that can simultaneously be transmitted at an identicalfrequency (common frequency). The radio processor multiplexes eachtransmitted signal in a frequency direction as needed basis, namely,performs a multi-carrier modulation (for example, OFDM scheme)), andinserts a pilot signal that is used when the receiver estimates atransmission path distortion, a frequency offset, and a phasedistortion. (Alternatively, the pilot signal may be used to estimateanother distortion, or the pilot signal may be used to detect a signalin the receiver. A usage mode of the pilot signal in the receiver is notlimited to the above estimations or the signal detection.) Thetransmitting antenna transmits z1(t) and z2(t) using two antennas (TX1and TX2).

The receiver includes receiving antennas (RX1 and RX2), a radioprocessor, a channel variation estimator, and a signal processor.Receiving antenna (RX1) receives the signals transmitted from twotransmitting antennas (TX1 and TX2) of the transmitter. The channelvariation estimator estimates a channel variation using the pilotsignal, and supplies an estimated value of the channel variation to thesignal processor. Based on channel values estimated as the signalsreceived by the two receiving antennas, the signal processor restorespieces of data included in z1(t) and z2(t), and obtains the pieces ofdata as one piece of received data. The received data may be a harddecision value of “0” and “1” or a soft decision value such as alog-likelihood or a log-likelihood ratio.

Various coding methods such as a turbo code and an LDPC (Low-DensityParity-Check) code are used as the coding method (NPLs 1 and 2).

CITATION LIST Non-Patent Literature

-   NPL 1: R. G. Gallager, “Low-density parity-check codes,” IRE Trans.    Inform. Theory, IT-8, pp-21-28, 1962.-   NPL 2: “Performance analysis and design optimization of LDPC-coded    MIMO OFDM systems” IEEE Trans. Signal Processing, vol. 52, no. 2,    pp. 348-361, February 2004.-   NPL 3: C. Douillard, and C. Berrou, “Turbo codes with rate-m/(m+1)    constituent convolutional codes,” IEEE Trans. Commun., vol. 53, no.    10, pp. 1630-1638, October 2005.-   NPL 4: C. Berrou, “The ten-year-old turbo codes are entering into    service”, IEEE Communication Magazine, vol. 41, no. 8, pp. 110-116,    August 2003.-   NPL 5: DVB Document A122, Framing structure, channel coding and    modulation for a second generation digital terrestrial television    broadcasting system (DVB-T2), June 2008.-   NPL 6: D. J. C. Mackay, “Good error-correcting codes based on very    sparse matrices,” IEEE Trans. Inform. Theory, vol. 45, no. 2, pp    399-431, March 1999.-   NPL 7: S. M. Alamouti, “A simple transmit diversity technique for    wireless communications,” IEEE J. Select. Areas Commun., vol. 16,    no. 8, pp. 1451-1458, October 1998.-   NPL 8: V. Tarokh, H. Jafrkhani, and A. R. Calderbank, “Space-time    block coding for wireless communications: Performance results,”    IEEE J. Select. Areas Commun., vol. 17, no. 3, no. 3, pp. 451-460,    March 1999.

SUMMARY

In one general aspect, the techniques disclosed here feature atransmission method including: performing error correction coding on aninformation bit string to generate a code word having a number of bitsthat is greater than a predetermined integral multiple of (X+Y);modulating a first bit string in which the number of bits is thepredetermined integral multiple of (X+Y) in the code word using a firstscheme, the first scheme being a set of a modulation scheme in whichmapping an X-bit bit string to generate a first complex signal and amodulation scheme in which mapping a Y-bit bit string to generate asecond complex signal; and modulating a second bit string in which thefirst bit string is removed from the code word using a second schemedifferent from the first scheme.

Additional benefits and advantages of the disclosed embodiments willbecome apparent from the specification and drawings. The benefits and/oradvantages may be individually obtained by the various embodiments andfeatures of the specification and drawings, which need not all beprovided in order to obtain one or more of such benefits and/oradvantages.

It should be noted that general or specific embodiments may beimplemented as a system, a method, an integrated circuit, a computerprogram, a storage medium, or any selective combination thereof.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a view illustrating an arrangement example of QPSK signalpoints in an I-Q plane;

FIG. 2 is a view illustrating an arrangement example of 16QAM signalpoints in the I-Q plane;

FIG. 3 is a view illustrating an arrangement example of 64QAM signalpoints in the I-Q plane;

FIG. 4 is a view illustrating an arrangement example of 256QAM signalpoints in the I-Q plane;

FIG. 5 is a view illustrating a configuration example of a transmitter;

FIG. 6 is a view illustrating a configuration example of thetransmitter;

FIG. 7 is a view illustrating a configuration example of thetransmitter;

FIG. 8 is a view illustrating a configuration example of a signalprocessor;

FIG. 9 is a view illustrating an example of a frame configuration;

FIG. 10 is a view illustrating an arrangement example of the signalpoints of 16QAM in the I-Q plane;

FIG. 11 is a view illustrating an arrangement example of the signalpoints of 64QAM in the I-Q plane;

FIG. 12 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 13 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 14 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 15 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 16 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 17 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 18 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 19 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 20 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 21 is a view illustrating an arrangement example of the signalpoints in a first quadrant of the I-Q plane;

FIG. 22 is a view illustrating an arrangement example of the signalpoints in a second quadrant of the I-Q plane;

FIG. 23 is a view illustrating an arrangement example of the signalpoints in a third quadrant of the I-Q plane;

FIG. 24 is a view illustrating an arrangement example of the signalpoints in a fourth quadrant of the I-Q plane;

FIG. 25 is a view illustrating an arrangement example of the signalpoints in the first quadrant of the I-Q plane;

FIG. 26 is a view illustrating an arrangement example of the signalpoints in the second quadrant of the I-Q plane;

FIG. 27 is a view illustrating an arrangement example of the signalpoints in the third quadrant of the I-Q plane;

FIG. 28 is a view illustrating an arrangement example of the signalpoints in the fourth quadrant of the I-Q plane;

FIG. 29 is a view illustrating an arrangement example of the signalpoints in the first quadrant of the I-Q plane;

FIG. 30 is a view illustrating an arrangement example of the signalpoints in the second quadrant of the I-Q plane;

FIG. 31 is a view illustrating an arrangement example of the signalpoints in the third quadrant of the I-Q plane;

FIG. 32 is a view illustrating an arrangement example of the signalpoints in the fourth quadrant of the I-Q plane;

FIG. 33 is a view illustrating an arrangement example of the signalpoints in the first quadrant of the I-Q plane;

FIG. 34 is a view illustrating an arrangement example of the signalpoints in the second quadrant of the I-Q plane;

FIG. 35 is a view illustrating an arrangement example of the signalpoints in the third quadrant of the I-Q plane;

FIG. 36 is a view illustrating an arrangement example of the signalpoints in the fourth quadrant of the I-Q plane;

FIG. 37 is a view illustrating an arrangement example of the signalpoints in the first quadrant of the I-Q plane;

FIG. 38 is a view illustrating an arrangement example of the signalpoints in the second quadrant of the I-Q plane;

FIG. 39 is a view illustrating an arrangement example of the signalpoints in the third quadrant of the I-Q plane;

FIG. 40 is a view illustrating an arrangement example of the signalpoints in the fourth quadrant of the I-Q plane;

FIG. 41 is a view illustrating an arrangement example of the signalpoints in the first quadrant of the I-Q plane;

FIG. 42 is a view illustrating an arrangement example of the signalpoints in the second quadrant of the I-Q plane;

FIG. 43 is a view illustrating an arrangement example of the signalpoints in the third quadrant of the I-Q plane;

FIG. 44 is a view illustrating an arrangement example of the signalpoints in the fourth quadrant of the I-Q plane;

FIG. 45 is a view illustrating an arrangement example of the signalpoints in the first quadrant of the I-Q plane;

FIG. 46 is a view illustrating an arrangement example of the signalpoints in the second quadrant of the I-Q plane;

FIG. 47 is a view illustrating an arrangement example of the signalpoints in the third quadrant of the I-Q plane;

FIG. 48 is a view illustrating an arrangement example of the signalpoints in the fourth quadrant of the I-Q plane;

FIG. 49 is a view illustrating an arrangement example of the signalpoints in the first quadrant of the I-Q plane;

FIG. 50 is a view illustrating an arrangement example of the signalpoints in the second quadrant of the I-Q plane;

FIG. 51 is a view illustrating an arrangement example of the signalpoints in the third quadrant of the I-Q plane;

FIG. 52 is a view illustrating an arrangement example of the signalpoints in the fourth quadrant of the I-Q plane;

FIG. 53 is a view illustrating a relationship between a transmittingantenna and a receiving antenna;

FIG. 54 is a view illustrating a configuration example of a receiver;

FIG. 55 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 56 is a view illustrating an arrangement example of the signalpoints in the I-Q plane;

FIG. 57 is a configuration diagram illustrating a section that generatesa modulated signal in a transmitter according to a first exemplaryembodiment;

FIG. 58 is a flowchart illustrating a modulated signal generatingmethod;

FIG. 59 is a flowchart illustrating bit length adjustment processing ofthe first exemplary embodiment;

FIG. 60 is a view illustrating a configuration of a modulator accordingto a second exemplary embodiment;

FIG. 61 is a view illustrating an example of a parity check matrix;

FIG. 62 is a view illustrating a configuration example of a partialmatrix;

FIG. 63 is a flowchart illustrating LDPC coding processing performedwith encoder 502LA;

FIG. 64 is a view illustrating a configuration example performingaccumulate processing;

FIG. 65 is a flowchart illustrating bit length adjustment processing ofthe second exemplary embodiment;

FIG. 66 is a view illustrating an example of a method for generating abit string for adjustment;

FIG. 67 is a view illustrating an example of the method for generatingthe bit string for adjustment;

FIG. 68 is a view illustrating an example of the method for generatingthe bit string for adjustment;

FIG. 69 is a view illustrating a modification of an adjustment bitstring generated with a bit length adjuster;

FIG. 70 is a view illustrating a modification of the adjustment bitstring generated with the bit length adjuster;

FIG. 71 is a view illustrating one of perceptions according to thedisclosure associated with the second exemplary embodiment;

FIG. 72 is a view illustrating an outline of an MIMO system;

FIG. 73 is a view illustrating a configuration of a modulator accordingto a third exemplary embodiment;

FIG. 74 is a view illustrating operation of bit interleaver 502BI usingan output bit string;

FIG. 75 is a view illustrating an example of mounting bit interleaver502;

FIG. 76 is a view illustrating an example of the bit length adjustmentprocessing;

FIG. 77 is a view illustrating an example of the added bit string;

FIG. 78 is a view illustrating an example of insertion of the bit stringadjuster;

FIG. 79 is a view illustrating a modification of a configuration of themodulator;

FIG. 80 is a configuration diagram illustrating a modulator according toa fourth exemplary embodiment;

FIG. 81 is a flowchart illustrating processing;

FIG. 82 is a view illustrating a relationship between a length of K bitsof BB FRAME and an ensured length of TmpPadNum;

FIG. 83 is a configuration diagram illustrating a modulator differentfrom the modulator in FIG. 80 ;

FIG. 84 is a view illustrating bit lengths of bit strings 501 to 8003;

FIG. 85 is a view illustrating an example of a bit string decoder of thereceiver;

FIG. 86 is a view illustrating input and output of the bit stringadjuster;

FIG. 87 is a view illustrating an example of the bit string decoder ofthe receiver;

FIG. 88 is a view illustrating an example of the bit string decoder ofthe receiver;

FIG. 89 is a view conceptually illustrating processing according to asixth exemplary embodiment;

FIG. 90 is a view illustrating a relationship between the transmitterand the receiver;

FIG. 91 is a view illustrating a configuration example of atransmission-side modulator;

FIG. 92 is a view illustrating a bit length of each bit string;

FIG. 93 is a configuration diagram illustrating a transmission-sidemodulator different from the modulator in FIG. 91 ;

FIG. 94 is a view illustrating the bit length of each bit string;

FIG. 95 is a view illustrating the bit length of each bit string;

FIG. 96 is a view illustrating an example of the bit string decoder ofthe receiver;

FIG. 97 is a view illustrating a section that performsprecoding-associated processing;

FIG. 98 is a view illustrating the section that performs theprecoding-associated processing;

FIG. 99 is a view illustrating a configuration example of the signalprocessor;

FIG. 100 is a view illustrating an example of a frame configuration attime-frequency when two streams are transmitted;

FIG. 101A is a view illustrating a state of output first bit string 503;

FIG. 101B is a view illustrating a state of output second bit string5703;

FIG. 102A is a view illustrating the state of output first bit string503;

FIG. 102B is a view illustrating the state of output second bit string5703;

FIG. 103A is a view illustrating a state of output first bit string503Λ;

FIG. 103B is a view illustrating a state of output bit-length-adjustedbit string 7303;

FIG. 104A is a view illustrating a state of output first bit string 503′(or 503Λ);

FIG. 104B is a view illustrating a state of output bit-length-adjustedbit string 8003;

FIG. 105A is a view illustrating a state of output N-bit code word 503;

FIG. 105B is a view illustrating a state of output (N-PunNum)-bit datastring 9102;

FIG. 106 is a view illustrating an outline of the frame configuration;

FIG. 107 is a view illustrating an example in which at least two kindsof signals exist at an identical clock time;

FIG. 108 is a view illustrating a configuration example of thetransmitter;

FIG. 109 is a view illustrating an example of the frame configuration;

FIG. 110 is a view illustrating a configuration example of the receiver;

FIG. 111 is a view illustrating an arrangement example of the 16QAMsignal points in the I-Q plane;

FIG. 112 is a view illustrating an arrangement example of the 64QAMsignal points in the I-Q plane;

FIG. 113 is a view illustrating an arrangement example of the 256QAMsignal points in the I-Q plane;

FIG. 114 is a view illustrating an arrangement example of the 16QAMsignal points in the I-Q plane;

FIG. 115 is a view illustrating an arrangement example of the 64QAMsignal points in the I-Q plane;

FIG. 116 is a view illustrating an arrangement example of the 256QAMsignal points in the I-Q plane;

FIG. 117 is a view illustrating a configuration example of thetransmitter;

FIG. 118 is a view illustrating a configuration example of the receiver;

FIG. 119 is a view illustrating an arrangement example of the 16QAMsignal points in the I-Q plane;

FIG. 120 is a view illustrating an arrangement example of the 64QAMsignal points in the I-Q plane;

FIG. 121 is a view illustrating an arrangement example of the 256QAMsignal points in the I-Q plane;

FIG. 122 is a view illustrating a configuration example of thetransmitter;

FIG. 123 is a view illustrating an example of the frame configuration;

FIG. 124 is a view illustrating a configuration example of the receiver;

FIG. 125 is a view illustrating a configuration example of thetransmitter;

FIG. 126 is a view illustrating an example of the frame configuration;

FIG. 127 is a view illustrating a configuration example of the receiver;

FIG. 128 is a view illustrating a transmission method in which aspace-time block code is used;

FIG. 129 is a view illustrating a configuration example of thetransmitter;

FIG. 130 is a view illustrating a configuration example of thetransmitter;

FIG. 131 is a view illustrating a configuration example of thetransmitter;

FIG. 132 is a view illustrating a configuration example of thetransmitter;

FIG. 133 is a view illustrating the transmission method in which thespace-time block code is used;

FIG. 134 is a view illustrating a configuration example of thetransmitter;

FIG. 135 is a view illustrating an example of mapping processing;

FIG. 136 is a view illustrating an example of the mapping processing;

FIG. 137 is a view illustrating an example of the mapping processing;

FIG. 138 is a view illustrating an example of the mapping processing;

FIG. 139 is a view illustrating an example of the mapping processing;

FIG. 140 is a view illustrating an example of the mapping processing;

FIG. 141 is a view illustrating an example of the mapping processing;

FIG. 142 is a view illustrating an example of the mapping processing;

FIG. 143 is a view illustrating an example of the mapping processing;

FIG. 144 is a view illustrating an example of the mapping processing;

FIG. 145 is a view illustrating an example of the mapping processing;

FIG. 146 is a view illustrating an example of the mapping processing;

FIG. 147 is a view illustrating an example of the mapping processing;

FIG. 148 is a view illustrating an example of the mapping processing;

FIG. 149 is a view illustrating an example of the mapping processing;

FIG. 150 is a view illustrating the transmission method in which thespace-time block code is used;

FIG. 151 is a view illustrating an example of the mapping processing;

FIG. 152 is a view illustrating an example of the mapping processing;

FIG. 153 is a view illustrating an example of the mapping processing;

FIG. 154 is a view illustrating an example of the mapping processing;

FIG. 155 is a view illustrating an example of the mapping processing;

FIG. 156 is a view illustrating an example of the mapping processing;

FIG. 157 is a view illustrating an example of the mapping processing;

FIG. 158 is a view illustrating an example of the mapping processing;

FIG. 159 is a view illustrating an example of the mapping processing;

FIG. 160 is a view illustrating an example of the mapping processing;and

FIG. 161 is a view illustrating the transmission method in which thespace-time block code is used.

DETAILED DESCRIPTION

A transmission method and a reception method, to which the exemplaryembodiments of the present disclosure can be applied, and configurationexamples of a transmitter and a receiver, in which the transmissionmethod and reception method are used, will be described below in advanceof the description of exemplary embodiments of the present disclosure.

Configuration Example R1

FIG. 5 illustrates a configuration example of a portion that generates amodulated signal when the transmitter of a base station (such as abroadcasting station and an access point) can change a transmissionscheme.

In the configuration example of FIG. 5 , there is a transmission methodfor transmitting two streams (MIMO (Multiple Input Multiple Output)scheme) as one of changeable transmission schemes.

The transmission method in the case that the transmitter of the basestation (such as the broadcasting station and the access point)transmits two streams will be described with reference to FIG. 5 .

In FIG. 5 , information 501 and control signal 512 are input to encoder502, and encoder 502 performs coding based on information about a codingrate and a code length (block length) included in control signal 512,and outputs coded data 503.

Coded data 503 and control signal 512 are input to mapper 504. It isassumed that control signal 512 assigns the transmission of the twostreams as a transmission scheme. Additionally, it is assumed thatcontrol signal 512 assigns modulation scheme α and modulation scheme βas respective modulation schemes of the two streams. It is assumed thatmodulation scheme α is a modulation scheme for modulating x-bit data,and that modulation scheme β is a modulation scheme for modulating y-bitdata (for example, a modulation scheme for modulating 4-bit data for16QAM (16 Quadrature Amplitude Modulation), and a modulation scheme formodulating 6-bit data for 64QAM (64 Quadrature Amplitude Modulation)).

Mapper 504 modulates the x-bit data in (x+y)-bit data using modulationscheme α to generate and output baseband signal s₁(t) (505A), andmodulates the remaining y-bit data using modulation scheme β to outputbaseband signal s₂(t) (505B). (One mapper is provided in FIG. 5 .Alternatively, a mapper that generates baseband signal s₁(t) and amapper that generates baseband signal s₂(t) may separately be provided.At this point, coded data 503 is divided in the mapper that generatesbaseband signal s₁(t) and the mapper that generates baseband signals₂(t).)

Each of s₁(t) and s₂(t) is represented as a complex number (however, maybe one of a complex number and a real number), and t is time. For thetransmission scheme in which multi-carrier such as OFDM (OrthogonalFrequency Division Multiplexing) is used, it can also be considered thats₁ and s₂ are a function of frequency f like s₁(f) and s₂(f) or that s₁and s₂ are a function of time t and frequency f like s₁(t,f) ands₂(t,f).

Hereinafter, the baseband signal, a precoding matrix, a phase change,and the like are described as the function of time t. Alternatively, thebaseband signal, the precoding matrix, the phase change, and the likemay be considered to be the function of frequency f or the function oftime t and frequency f.

Accordingly, sometimes the baseband signal, the precoding matrix, thephase change, and the like are described as a function of symbol numberi. In this case, the baseband signal, the precoding matrix, the phasechange, and the like may be considered to be the function of time t, thefunction of frequency f, or the function of time t and frequency f. Thatis, the symbol and the baseband signal may be generated and disposed ineither a time-axis direction or a frequency-axis direction. The symboland the baseband signal may be generated and disposed in the time-axisdirection and the frequency-axis direction.

Baseband signal s₁(t) (505A) and control signal 512 are input to powerchanger 506A (power adjuster 506A), and power changer 506A (poweradjuster 506A) sets real number P₁ based on control signal 512, andoutputs (P₁×s₁(t)) as power-changed signal 507A (P₁ may be a complexnumber).

Similarly, baseband signal s₂(t) (505B) and control signal 512 are inputto power changer 506B (power adjuster 506B), and power changer 506B(power adjuster 506B) sets real number P₂, and outputs P₂×s₂(t) aspower-changed signal 507B (P₂ may be a complex number).

Power-changed signal 507A, power-changed signal 507B, and control signal512 are input to weighting synthesizer 508, and weighting synthesizer508 sets precoding matrix F (or F(i)) based on control signal 512.Assuming that i is a slot number (symbol number), weighting synthesizer508 performs the following calculation.

[Mathematical  formula  1] $\begin{matrix}\begin{matrix}{\begin{pmatrix}{u_{1}(i)} \\{u_{2}(i)}\end{pmatrix} = {F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} \\{= {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} \\{= {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}\end{matrix} & ({R1})\end{matrix}$

In the formula, each of a(i), b(i), c(i), and d(i) is represented as acomplex number (may be represented as a real number), and at least threeof a(i), b(i), c(i), and d(i) must not be 0 (zero). The precoding matrixmay be a function of i or does not need to be the function of i. Whenthe precoding matrix is the function of i, the precoding matrix isswitched by a slot number (symbol number).

Weighting synthesizer 508 outputs u₁(i) in equation (R1) asweighting-synthesized signal 509A, and outputs u₂(i) in equation (R1) asweighting-synthesized signal 509B.

Weighting-synthesized signal 509A (u₁(i)) and control signal 512 areinput to power changer 510A, and power changer 510A sets real number Q₁based on control signal 512, and outputs (Q₁ (Q₁ is a realnumber)×u₁(t)) as power-changed signal 511A (z₁(i)) (alternatively, Q₁may be a complex number).

Similarly, weighting-synthesized signal 509B (u₂(i)) and control signal512 are input to power changer 510B, and power changer 510B sets realnumber Q₂ based on control signal 512, and outputs (Q₂ (Q₂ is a realnumber)×u₂(t)) as power-changed signal 511A (z₂(i)) (alternatively, Q₂may be a complex number).

Accordingly, the following equation holds.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{f{ormula}}\mspace{14mu} 2} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & ({R2})\end{matrix}$

The transmission method in the case that two streams different fromthose in FIG. 5 will be described with reference to FIG. 6 . In FIG. 6 ,the component similar to that in FIG. 5 is designated by the identicalreference mark.

Signal 509B in which u₂(i) in equation (R1) is weighting-synthesized andcontrol signal 512 are input to phase changer 601, and phase changer 601changes a phase of signal 509B in which u₂(i) in equation (R1) isweighting-synthesized based on control signal 512. Accordingly, thesignal in which the phase of signal 509B in which u₂(i) in equation (R1)is weighting-synthesized is represented as (e^(jθ(i))×u₂(i)), and phasechanger 601 outputs (e^(jθ(i))×u₂(i)) as phase-changed signal 602 (j isan imaginary unit). The changed phase constitutes a characteristicportion that the changed phase is the function of i like θ(i).

Each of power changers 510A and 510B in FIG. 6 changes power of theinput signal. Accordingly, outputs z₁(i) and z₂(i) of power changers510A and 510B in FIG. 6 are given by the following equation.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{f{ormula}}\mspace{14mu} 3} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & ({R3})\end{matrix}$

FIG. 7 illustrates a configuration different from that in FIG. 6 as amethod for performing equation (R3). A difference between theconfigurations in FIGS. 6 and 7 is that the positions of the powerchanger and phase changer are exchanged (the function of changing thepower and the function of changing the phase are not changed). At thispoint, z₁(i) and z₂(i) are given by the following equation.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{f{ormula}}\mspace{14mu} 4} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} = {{\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & ({R4})\end{matrix}$

z₁(i) in equation (R3) is equal to z₁(i) in equation (R4), and z₂(i) inequation (R3) is equal to z₂(i) in equation (R4).

As to phase value θ(i) to be changed in equations (R3) and (R4),assuming that θ(i+1)-θ(i) is set to a fixed value, there is a highpossibility that the receiver obtains the good data reception quality ina radio wave propagation environment where a direct wave is dominant.However, a method for providing phase value θ(i) to be changed is notlimited to the above example.

FIG. 8 illustrates a configuration example of a signal processor thatprocesses signals z₁(i) and z₂(i) obtained in FIGS. 5 to 7 .

Signal z₁(i) (801A), pilot symbol 802A, control information symbol 803A,and control signal 512 are input to inserter 804A, and inserter 804Ainserts pilot symbol 802A and control information symbol 803A in signal(symbol) z₁(i) (801A) according to a frame configuration included incontrol signal 512, and outputs modulated signal 805A according to theframe configuration.

Pilot symbol 802A and control information symbol 803A are a symbolmodulated using BPSK (Binary Phase Shift Keying), QPSK (Quadrature PhaseShift Keying), and the like (other modulation schemes may be used).

Modulated signal 805A and control signal 512 are input to radio section806A, and radio section 806A performs pieces of processing such asfrequency conversion and amplification on modulated signal 805A based oncontrol signal 512 (performs inverse Fourier transform when the OFDMscheme is used), and outputs transmitted signal 807A as a radio wavefrom antenna 808A.

Signal z₂(i) (801B), pilot symbol 802B, control information symbol 803B,and control signal 512 are input to inserter 804B, and inserter 804Binserts pilot symbol 802B and control information symbol 803B in signal(symbol) z₂(i) (801B) according to the frame configuration included incontrol signal 512, and outputs modulated signal 805B according to theframe configuration.

Pilot symbol 802B and control information symbol 803B are a symbolmodulated using BPSK (Binary Phase Shift Keying), QPSK (Quadrature PhaseShift Keying), and the like (other modulation schemes may be used).

Modulated signal 805B and control signal 512 are input to radio section806B, and radio section 806B performs the pieces of processing such asthe frequency conversion and the amplification on modulated signal 805Bbased on control signal 512 (performs the inverse Fourier transform whenthe OFDM scheme is used), and outputs transmitted signal 807B as a radiowave from antenna 808B.

Signals z₁(i) (801A) and z₂(i) (801B) having the identical number of iare transmitted from different antennas at the identical time and theidentical (common) frequency (that is, the transmission method in whichthe MIMO scheme is used).

Pilot symbols 802A and 802B are a symbol that is used when the receiverperforms the signal detection, the estimation of the frequency offset,gain control, the channel estimation, and the like. Although the symbolis named the pilot symbol in this case, the symbol may be named othernames such as a reference symbol.

Control information symbols 803A and 803B are a symbol that transmitsthe information about the modulation scheme used in the transmitter, theinformation about the transmission scheme, the information about theprecoding scheme, the information about an error correction code scheme,the information about the coding rate of an error correction code, andthe information about a block length (code length) of the errorcorrection code to the receiver. The control information symbol may betransmitted using only one of control information symbols 803A and 803B.

FIG. 9 illustrates an example of the frame configuration attime-frequency when the two streams are transmitted. In FIG. 9 , ahorizontal axis indicates a frequency, a vertical axis indicates time.FIG. 9 illustrates a configuration of the symbol from carriers 1 to 38from clock time $1 to clock time $11.

FIG. 9 simultaneously illustrates the frame configuration of thetransmitted signal transmitted from antenna 808A in FIG. 8 and the frameof the transmitted signal transmitted from antenna 808B in FIG. 8 .

In FIG. 9 , a data symbol corresponds to signal (symbol) z₁(i) for theframe of the transmitted signal transmitted from antenna 808A in FIG. 8. The pilot symbol corresponds to pilot symbol 802A.

In FIG. 9 , a data symbol corresponds to signal (symbol) z₂(i) for theframe of the transmitted signal transmitted from antenna 808B in FIG. 8. The pilot symbol corresponds to pilot symbol 802B.

Accordingly, as described above, signals z₁(i) (801A) and z₂(i) (801B)having the identical number of i are transmitted from different antennasat the identical time and the identical (common) frequency. Theconfiguration of the pilot symbol is not limited to that in FIG. 9 . Forexample, a time interval and a frequency interval of the pilot symbolare not limited to those in FIG. 9 . In FIG. 9 , the pilot symbols aretransmitted at the identical clock time and the identical frequency(identical (sub-) carrier) from antennas 808A and 808B in FIG. 8 .Alternatively, for example, the pilot symbol may be disposed in notantenna 808B in FIG. 8 but antenna 808A in FIG. 8 at time A andfrequency a ((sub-) carrier a), and the pilot symbol may be disposed innot antenna 808A in FIG. 8 but antenna 808B in FIG. 8 at time B andfrequency b ((sub-) carrier b).

Although only the data symbol and the pilot symbol are illustrated inFIG. 9 , other symbols such as a control information symbol may beincluded in the frame.

Although the case that a part (or whole) of the power changer exists isdescribed with reference to FIGS. 5 to 7 , it is also considered that apart of the power changer is missing.

For example, in the case that power changer 506A (power adjuster 506A)and power changer 506B (power adjuster 506B) do not exist in FIG. 5 ,z₁(i) and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 5} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & ({R5})\end{matrix}$

In the case that power changer 510A (power adjuster 510A) and powerchanger 510B (power adjuster 510B) do not exist in FIG. 5 , z₁(i) andz₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 6} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & ({R6})\end{matrix}$

In the case that power changer 506A (power adjuster 506A), power changer506B (power adjuster 506B), power changer 510A (power adjuster 510A),and power changer 510B (power adjuster 510B) do not exist in FIG. 5 ,z₁(i) and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 7} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & ({R7})\end{matrix}$

In the case that power changer 506A (power adjuster 506A) and powerchanger 15506B (power adjuster 506B) do not exist in FIG. 6 or 7 , z₁(i)and z₂(i) are given as follows.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{f{ormula}}\mspace{14mu} 8} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & ({R8})\end{matrix}$

In the case that power changer 510A (power adjuster 510A) and powerchanger 510B (power adjuster 510B) do not exist in FIG. 6 or 7 , z₁(i)and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 9} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & ({R9})\end{matrix}$

In the case that power changer 506A (power adjuster 506A), power changer506B (power adjuster 506B), power changer 510A (power adjuster 510A),and power changer 510B (power adjuster 510B) do not exist in FIG. 6 or 7, z₁(i) and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 10} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}1 & 0 \\0 & e^{{j\theta}{(i)}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & ({R10})\end{matrix}$

QPSK, 16QAM, 64QAM, and 256QAM mapping methods will be described belowas an example of the mapping method of a modulation scheme forgenerating baseband signal s₁(t) (505A) and baseband signal s₂(t)(505B).

The QPSK mapping method will be described below. FIG. 1 illustrates anexample of signal point arrangement of QPSK signal points in anin-phase-quadrature-phase plane (I-Q plane). In FIG. 1 , 4 marks “◯”indicate QPSK signal points, a horizontal axis indicates I, and avertical axis indicates Q.

In the I-Q plane, 4 signal points included in QPSK (indicated by themarks “◯” in FIG. 1 ) are (w_(q),w_(q)), (−w_(q),w_(q)), (w_(q),−w_(q)),and (−w_(q),−w_(q)) (w_(q) is a real number larger than 0).

At this point, bits to be transmitted (input bits) are set to b0 and b1.For example, for the bits to be transmitted (b0, b1)=(0,0), the bits aremapped at signal point 101 in FIG. 1 , and (I,Q)=(w_(q),w_(q)) isobtained when I is an in-phase component while Q is a quadraturecomponent of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1), in-phase component I andquadrature component Q of the mapped baseband signal are decided (duringQPSK modulation). FIG. 1 illustrates an example of a relationshipbetween the set of b0 and b1 (00 to 11) and the signal pointcoordinates. Values 00 to 11 of the set of b0 and b1 are indicatedimmediately below 4 signal points included in QPSK (indicated by themarks “◯” in FIG. 1 ) (w_(q),w_(q)), (−w_(q),w_(q)), (w_(q),−w_(q)), and(−w_(q),−w_(q)). Respective coordinates of the signal points (“◯”)immediately above the values 00 to 11 of the set of b0 and b1 in the I-Qplane serve as in-phase component I and quadrature component Q of themapped baseband signal. The relationship between the set of b0 and b1(00 to 11) and the signal point coordinates during QPSK is not limitedto that in FIG. 1 . A complex value of in-phase component I andquadrature component Q of the mapped baseband signal (during QPSKmodulation) serves as a baseband signal (s₁(t) or s₂(t)).

The 16QAM mapping method will be described below. FIG. 2 illustrates anarrangement example of 16QAM signal points in the I-Q plane. In FIG. 2 ,16 marks “◯” indicate 16QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 16 signal points included in 16QAM (indicated by themarks “◯” in FIG. 2 ) the I-Q are obtained as follows. (w₁₆ is a realnumber larger than 0.) (3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆),(3w₁₆,−3w₁₆), (w₁₆,3w₁₆), (w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆),(−w₁₆,3w₁₆), (−w₁₆,w₁₆), (−w₁₆,−w₁₆), (−w₁₆,−3w₁₆), (−3w₁₆,3w₁₆),(−3w₁₆,w₁₆), (−3w₁₆,−w₁₆), (−3w₁₆,−3w₁₆)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, and b3. For example, for the bits to be transmitted (b0, b1, b2,b3)=(0, 0, 0, 0), the bits are mapped at signal point 201 in FIG. 2 ,and (I,Q)=(3w₁₆,3w₁₆) is obtained when I is an in-phase component whileQ is a quadrature component of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3), in-phase componentI and quadrature component Q of the mapped baseband signal are decided(during 16QAM modulation). FIG. 2 illustrates an example of arelationship between the set of b0, b1, b2, and b3 (0000 to 1111) andthe signal point coordinates. Values 0000 to 1111 of the set of b0, b1,b2, and b3 are indicated immediately below 16 signal points included in16QAM (the marks “◯” in FIG. 2 ) (3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆),(3w₁₆,−3w₁₆), (w₁₆,3w₁₆), (w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆),(−w₁₆,3w₁₆), (−w₁₆,w₁₆), (−w₁₆, −w₁₆), (−w₁₆,−3w₁₆), (−3w₁₆,3w₁₆),(−3w₁₆,w₁₆), (−3w₁₆,−w₁₆), (−3w₁₆,−3w₁₆). Respective coordinates of thesignal points (“◯”) immediately above the values 0000 to 1111 of the setof b0, b1, b2, and b3 in the I-Q plane serve as in-phase component I andquadrature component Q of the mapped baseband signal. The relationshipbetween the set of b0, b1, b2, and b3 (0000 to 1111) and the signalpoint coordinates during 16QAM modulation is not limited to that in FIG.2 . A complex value of in-phase component I and quadrature component Qof the mapped baseband signal (during 16QAM modulation) serves as abaseband signal (s₁(t) or s₂(t)).

The 64QAM mapping method will be described below. FIG. 3 illustrates anarrangement example of 64QAM signal points in the I-Q plane. In FIG. 3 ,64 marks “◯” indicate 64QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 64 signal points included in 64QAM (indicated by themarks “◯” in FIG. 3 ) the I-Q are obtained as follows. (w₆₄ is a realnumber larger than 0)

(7w₆₄,7w₆₄), (7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄),(7w₆₄,−3w₆₄), (7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄) (5w₆₄,7w₆₄), (5w₆₄,5w₆₄),(5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄), (5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄),(5w₆₄,−7w₆₄) (3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄),(3w₆₄,−w₆₄), (3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄)(−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄), (−w₆₄,w₆₄), (−w₆₄,−w₆₄),(−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄−7w₆₄)(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, for the bits to be transmitted (b0,b1, b2, b3, b4, b5)=(0, 0, 0, 0, 0, 0), the bits are mapped at signalpoint 301 in FIG. 3 , and (I,Q)=(7w₆₄,7w₆₄) is obtained when I is anin-phase component while Q is a quadrature component of the mappedbaseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 3 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to 111111 of theset of b0, b1, b2, b3, b4, and b5 are indicated immediately below 64signal points included in 64QAM (the marks “◯” in FIG. 3 ) (7w₆₄,7w₆₄),(7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄), (7w₆₄,−3w₆₄),(7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄)

(−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄), (−w₆₄,w₆₄), (−w₆₄,−w₆₄),(−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄,−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄). Respective coordinates ofthe signal points (“◯”) immediately above the values 000000 to 111111 ofthe set of b0, b1, b2, b3, b4, and b5 in the I-Q plane serve as in-phasecomponent I and quadrature component Q of the mapped baseband signal.The relationship between the set of b0, b1, b2, b3, b4, and b5 (000000to 111111) and the signal point coordinates during 64QAM modulation isnot limited to that in FIG. 3 . A complex value of in-phase component Iand quadrature component Q of the mapped baseband signal (during 64QAMmodulation) serves as a baseband signal (s₁(t) or s₂(t)).

The 256QAM mapping method will be described below. FIG. 4 illustrates anarrangement example of 256QAM signal points in the I-Q plane. In FIG. 4, 256 marks “◯” indicate the 256QAM signal points.

In the I-Q plane, 256 signal points included in 256QAM (indicated by themarks “◯” in FIG. 4 ) are obtained as follows. (w₂₅₆ is a real numberlarger than 0).

(15w₂₅₆,15w₂₅₆), (15w₂₅₆,13w₂₅₆), (15w₂₅₆,11w₂₅₆), (15w₂₅₆,9w₂₅₆),(15w₂₅₆,7w₂₅₆), (15w₂₅₆,5w₂₅₆), (15w₂₅₆,3w₂₅₆), (15w₂₅₆,w₂₅₆),(15w₂₅₆,−15w₂₅₆), (15w₂₅₆,−13w₂₅₆), (15w₂₅₆,−11w₂₅₆), (15w₂₅₆,−9w₂₅₆),(15w₂₅₆,−7w₂₅₆), (15w₂₅₆,−5w₂₅₆), (15w₂₅₆,−3w₂₅₆), (15w₂₅₆,−w₂₅₆),(13w₂₅₆,15w₂₅₆), (13w₂₅₆,13w₂₅₆), (13w₂₅₆,11w₂₅₆), (13w₂₅₆,9w₂₅₆),(13w₂₅₆,7w₂₅₆), (13w₂₅₆,5w₂₅₆), (13w₂₅₆,3w₂₅₆), (13w₂₅₆,w₂₅₆),(13w₂₅₆,−15w₂₅₆), (13w₂₅₆,−13w₂₅₆), (13w₂₅₆,−11w₂₅₆), (13w₂₅₆,−9w₂₅₆),(13w₂₅₆,−7w₂₅₆), (13w₂₅₆,−5w₂₅₆), (13w₂₅₆,−3w₂₅₆), (13w₂₅₆,−w₂₅₆),(11w₂₅₆,15w₂₅₆), (11w₂₅₆,13w₂₅₆), (11w₂₅₆,11w₂₅₆), (11w₂₅₆,9w₂₅₆),(11w₂₅₆,7w₂₅₆), (11w₂₅₆,5w₂₅₆), (11w₂₅₆,3w₂₅₆), (11w₂₅₆,w₂₅₆),(11w₂₅₆,−15w₂₅₆), (11w₂₅₆,−13w₂₅₆), (11w₂₅₆,−11w₂₅₆), (11w₂₅₆,−9w₂₅₆),(11w₂₅₆,−7w₂₅₆), (11w₂₅₆,−5w₂₅₆), (11w₂₅₆,−3w₂₅₆), (11w₂₅₆,−w₂₅₆),(9w₂₅₆,15w₂₅₆), (9w₂₅₆,13w₂₅₆), (9w₂₅₆,11w₂₅₆), (9w₂₅₆,9w₂₅₆),(9w₂₅₆,7w₂₅₆), (9w₂₅₆,5w₂₅₆), (9w₂₅₆,3w₂₅₆), (9w₂₅₆,w₂₅₆),(9w₂₅₆,−15w₂₅₆), (9w₂₅₆,−13w₂₅₆), (9w₂₅₆,−11w₂₅₆), (9w₂₅₆,−9w₂₅₆),(9w₂₅₆,−7w₂₅₆), (9w₂₅₆,−5w₂₅₆), (9w₂₅₆,−3w₂₅₆), (9w₂₅₆,−w₂₅₆),(7w₂₅₆,15w₂₅₆), (7w₂₅₆,13w₂₅₆), (7w₂₅₆,11w₂₅₆), (7w₂₅₆,9w₂₅₆),(7w₂₅₆,7w₂₅₆), (7w₂₅₆,5w₂₅₆), (7w₂₅₆,3w₂₅₆), (7w₂₅₆,w₂₅₆),(7w₂₅₆,−15w₂₅₆), (7w₂₅₆,−13w₂₅₆), (7w₂₅₆,−11w₂₅₆), (7w₂₅₆,−9w₂₅₆),(7w₂₅₆,−7w₂₅₆), (7w₂₅₆,−5w₂₅₆), (7w₂₅₆,−3w₂₅₆), (7w₂₅₆,−w₂₅₆),(5w₂₅₆,15w₂₅₆), (5w₂₅₆,13w₂₅₆), (5w₂₅₆,11w₂₅₆), (5w₂₅₆,9w₂₅₆),(5w₂₅₆,7w₂₅₆), (5w₂₅₆,5w₂₅₆), (5w₂₅₆,3w₂₅₆), (5w₂₅₆,w₂₅₆),(5w₂₅₆,−15w₂₅₆), (5w₂₅₆,−13w₂₅₆), (5w₂₅₆,−11w₂₅₆), (5w₂₅₆,−9w₂₅₆),(5w₂₅₆,−7w₂₅₆), (5w₂₅₆,−5w₂₅₆), (5w₂₅₆,−3w₂₅₆), (5w₂₅₆,−w₂₅₆),(3w₂₅₆,15w₂₅₆), (3w₂₅₆,13w₂₅₆), (3w₂₅₆,11w₂₅₆), (3w₂₅₆,9w₂₅₆),(3w₂₅₆,7w₂₅₆), (3w₂₅₆,5w₂₅₆), (3w₂₅₆,3w₂₅₆), (3w₂₅₆,w₂₅₆),(3w₂₅₆,−15w₂₅₆), (3w₂₅₆,−13w₂₅₆), (3w₂₅₆,−11w₂₅₆), (3w₂₅₆,−9w₂₅₆),(3w₂₅₆,−7w₂₅₆), (3w₂₅₆,−5w₂₅₆), (3w₂₅₆,−3w₂₅₆), (3w₂₅₆,−w₂₅₆),(w₂₅₆,15w₂₅₆), (w₂₅₆,13w₂₅₆), (w₂₅₆,11w₂₅₆), (w₂₅₆,9w₂₅₆), (w₂₅₆,7w₂₅₆),(w₂₅₆,5w₂₅₆), (w₂₅₆,3w₂₅₆), (w₂₅₆,w₂₅₆), (w₂₅₆,−15w₂₅₆), (w₂₅₆,−13w₂₅₆),(w₂₅₆,−11w₂₅₆), (w₂₅₆,−9w₂₅₆), (w₂₅₆,−7w₂₅₆), (w₂₅₆,−5w₂₅₆),(w₂₅₆,−3w₂₅₆), (w₂₅₆,−w₂₅₆),(−15w₂₅₆,15w₂₅₆), (−15w₂₅₆,13w₂₅₆), (−15w₂₅₆,11w₂₅₆), (−15w₂₅₆,9w₂₅₆),(−15w₂₅₆,7w₂₅₆), (−15w₂₅₆,5w₂₅₆), (−15w₂₅₆,3w₂₅₆), (−15w₂₅₆,w₂₅₆),(−15w₂₅₆,−15w₂₅₆), (−15w₂₅₆,−13w₂₅₆), (−15w₂₅₆,−11w₂₅₆),(−15w₂₅₆,−9w₂₅₆), (−15w₂₅₆,−7w₂₅₆), (−15w₂₅₆,−5w₂₅₆), (−15w₂₅₆,−3w₂₅₆),(−15w₂₅₆,−w₂₅₆),(−13w₂₅₆,15w₂₅₆), (−13w₂₅₆,13w₂₅₆), (−13w₂₅₆,11w₂₅₆), (−13w₂₅₆,9w₂₅₆),(−13w₂₅₆,7w₂₅₆), (−13w₂₅₆,5w₂₅₆), (−13w₂₅₆,3w₂₅₆), (−13w₂₅₆,w₂₅₆),(−13w₂₅₆,−15w₂₅₆), (−13w₂₅₆,−13w₂₅₆), (−13w₂₅₆,−11w₂₅₆),(−13w₂₅₆,−9w₂₅₆), (−13w₂₅₆,−7w₂₅₆), (−13w₂₅₆,−5w₂₅₆), (−13w₂₅₆,−3w₂₅₆),(−13w₂₅₆,−w₂₅₆),(−11w₂₅₆,15w₂₅₆), (−11w₂₅₆,13w₂₅₆), (−11w₂₅₆,11w₂₅₆), (−11w₂₅₆,9w₂₅₆),(−11w₂₅₆,7w₂₅₆), (−11w₂₅₆,5w₂₅₆), (−11w₂₅₆,3w₂₅₆), (−11w₂₅₆,w₂₅₆),(−11w₂₅₆,−15w₂₅₆), (−11w₂₅₆,−13w₂₅₆), (−11w₂₅₆,−11w₂₅₆),(−11w₂₅₆,−9w₂₅₆), (−11w₂₅₆,−7w₂₅₆), (−11w₂₅₆,−5w₂₅₆), (−11w₂₅₆,−3w₂₅₆),(−11w₂₅₆,−w₂₅₆),(−9w₂₅₆,15w₂₅₆), (−9w₂₅₆,13w₂₅₆), (−9w₂₅₆,11w₂₅₆), (−9w₂₅₆,9w₂₅₆),(−9w₂₅₆,7w₂₅₆), (−9w₂₅₆,5w₂₅₆), (−9w₂₅₆,3w₂₅₆), (−9w₂₅₆,w₂₅₆),(−9w₂₅₆,−15w₂₅₆), (−9w₂₅₆,−13w₂₅₆), (−9w₂₅₆,−11w₂₅₆), (−9w₂₅₆,−9w₂₅₆),(−9w₂₅₆,−7w₂₅₆), (−9w₂₅₆,−5w₂₅₆), (−9w₂₅₆,−3w₂₅₆), (−9w₂₅₆,−w₂₅₆),(−7w₂₅₆,15w₂₅₆), (−7w₂₅₆,13w₂₅₆), (−7w₂₅₆,11w₂₅₆), (−7w₂₅₆,9w₂₅₆),(−7w₂₅₆,7w₂₅₆), (−7w₂₅₆,5w₂₅₆), (−7w₂₅₆,3w₂₅₆), (−7w₂₅₆,w₂₅₆),(−7w₂₅₆,−15w₂₅₆), (−7w₂₅₆,−13w₂₅₆), (−7w₂₅₆,−11w₂₅₆), (−7w₂₅₆,−9w₂₅₆),(−7w₂₅₆,−7w₂₅₆), (−7w₂₅₆,−5w₂₅₆), (−7w₂₅₆,−3w₂₅₆), (−7w₂₅₆,−w₂₅₆),(−5w₂₅₆,15w₂₅₆), (−5w₂₅₆,13w₂₅₆), (−5w₂₅₆,11w₂₅₆), (−5w₂₅₆,9w₂₅₆),(−5w₂₅₆,7w₂₅₆), (−5w₂₅₆,5w₂₅₆), (−5w₂₅₆,3w₂₅₆), (−5w₂₅₆,w₂₅₆),(−5w₂₅₆,−15w₂₅₆), (−5w₂₅₆,−13w₂₅₆), (−5w₂₅₆,−11w₂₅₆), (−5w₂₅₆,−9w₂₅₆),(−5w₂₅₆,−7w₂₅₆), (−5w₂₅₆,−5w₂₅₆), (−5w₂₅₆,−3w₂₅₆), (−5w₂₅₆,−w₂₅₆),(−3w₂₅₆,15w₂₅₆), (−3w₂₅₆,13w₂₅₆), (−3w₂₅₆,11w₂₅₆), (−3w₂₅₆,9w₂₅₆),(−3w₂₅₆,7w₂₅₆), (−3w₂₅₆,5w₂₅₆), (−3w₂₅₆,3w₂₅₆), (−3w₂₅₆,w₂₅₆),(−3w₂₅₆,−15w₂₅₆), (−3w₂₅₆,−13w₂₅₆), (−3w₂₅₆,−11w₂₅₆), (−3w₂₅₆,−9w₂₅₆),(−3w₂₅₆,−7w₂₅₆), (−3w₂₅₆,−5w₂₅₆), (−3w₂₅₆,−3w₂₅₆), (−3w₂₅₆,−w₂₅₆),(−w₂₅₆,15w₂₅₆), (−w₂₅₆,13w₂₅₆), (−w₂₅₆,11w₂₅₆), (−w₂₅₆,9w₂₅₆),(−w₂₅₆,7w₂₅₆), (−w₂₅₆,5w₂₅₆), (−w₂₅₆,3w₂₅₆), (−w₂₅₆,w₂₅₆),(−w₂₅₆,−15w₂₅₆), (−w₂₅₆,−w₂₅₆), (−w₂₅₆,−11w₂₅₆), (−w₂₅₆,−9w₂₅₆),(−w₂₅₆,−7w₂₅₆), (−w₂₅₆,−5w₂₅₆), (−w₂₅₆,−3w₂₅₆), (−w₂₅₆,−w₂₅₆)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, b5, b6, and b7. For example, for the bits to betransmitted (b0, b1, b2, b3, b4, b5, b6, b7)=(0,0,0,0,0,0,0,0), the bitsare mapped at signal point 401 in FIG. 4 , and (I,Q)=(15w₂₅₆,15w₂₅₆) isobtained when I is an in-phase component while Q is a quadraturecomponent of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5, b6, b7),in-phase component I and quadrature component Q of the mapped basebandsignal are decided (during 256QAM modulation). FIG. 4 illustrates anexample of a relationship between the set of b0, b1, b2, b3, b4, b5, b6,and b7 (00000000 to 11111111) and the signal point coordinates. Values00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6, and b7are indicated immediately below 256 signal points included in 256QAM(the marks “◯” in FIG. 4 ) (15w₂₅₆,15w₂₅₆), (15w₂₅₆,13w₂₅₆),(15w₂₅₆,11w₂₅₆), (15w₂₅₆,9w₂₅₆), (15w₂₅₆,7w₂₅₆), (15w₂₅₆,5w₂₅₆),(15w₂₅₆,3w₂₅₆), (15w₂₅₆,w₂₅₆), (15w₂₅₆,−15w₂₅₆), (15w₂₅₆,−13w₂₅₆),(15w₂₅₆,−11w₂₅₆), (15w₂₅₆,−9w₂₅₆), (15w₂₅₆,−7w₂₅₆), (15w₂₅₆,−5w₂₅₆),(15w₂₅₆,−3w₂₅₆), (15w₂₅₆,−w₂₅₆),

(13w₂₅₆,15w₂₅₆), (13w₂₅₆,13w₂₅₆), (13w₂₅₆,11w₂₅₆), (13w₂₅₆,9w₂₅₆),(13w₂₅₆,7w₂₅₆), (13w₂₅₆,5w₂₅₆), (13w₂₅₆,3w₂₅₆), (13w₂₅₆,w₂₅₆),(13w₂₅₆,−15w₂₅₆), (13w₂₅₆,−13w₂₅₆), (13w₂₅₆,−11w₂₅₆), (13w₂₅₆,−9w₂₅₆),(13w₂₅₆,−7w₂₅₆), (13w₂₅₆,−5w₂₅₆), (13w₂₅₆,−3w₂₅₆), (13w₂₅₆,−w₂₅₆),(11w₂₅₆,15w₂₅₆), (11w₂₅₆,13w₂₅₆), (11w₂₅₆,11w₂₅₆), (11w₂₅₆,9w₂₅₆),(11w₂₅₆,7w₂₅₆), (11w₂₅₆,5w₂₅₆), (11w₂₅₆,3w₂₅₆), (11w₂₅₆,w₂₅₆),(11w₂₅₆,−15w₂₅₆), (11w₂₅₆,−13w₂₅₆), (11w₂₅₆,−11w₂₅₆), (11w₂₅₆,−9w₂₅₆),(11w₂₅₆,−7w₂₅₆), (11w₂₅₆,−5w₂₅₆), (11w₂₅₆,−3w₂₅₆), (11w₂₅₆,−w₂₅₆),(9w₂₅₆,15w₂₅₆), (9w₂₅₆,13w₂₅₆), (9w₂₅₆,11w₂₅₆), (9w₂₅₆,9w₂₅₆),(9w₂₅₆,7w₂₅₆), (9w₂₅₆,5w₂₅₆), (9w₂₅₆,3w₂₅₆), (9w₂₅₆,w₂₅₆),(9w₂₅₆,−15w₂₅₆), (9w₂₅₆,−13w₂₅₆), (9w₂₅₆,−11w₂₅₆), (9w₂₅₆,−9w₂₅₆),(9w₂₅₆,−7w₂₅₆), (9w₂₅₆,−5w₂₅₆), (9w₂₅₆,−3w₂₅₆), (9w₂₅₆,−w₂₅₆),(7w₂₅₆,15w₂₅₆), (7w₂₅₆,13w₂₅₆), (7w₂₅₆,11w₂₅₆), (7w₂₅₆,9w₂₅₆),(7w₂₅₆,7w₂₅₆), (7w₂₅₆,5w₂₅₆), (7w₂₅₆,3w₂₅₆), (7w₂₅₆,w₂₅₆),(7w₂₅₆,−15w₂₅₆), (7w₂₅₆,−13w₂₅₆), (7w₂₅₆,−11w₂₅₆), (7w₂₅₆,−9w₂₅₆),(7w₂₅₆,−7w₂₅₆), (7w₂₅₆,−5w₂₅₆), (7w₂₅₆,−3w₂₅₆), (7w₂₅₆,−w₂₅₆),(5w₂₅₆,15w₂₅₆), (5w₂₅₆,13w₂₅₆), (5w₂₅₆,11w₂₅₆), (5w₂₅₆,9w₂₅₆),(5w₂₅₆,7w₂₅₆), (5w₂₅₆,5w₂₅₆), (5w₂₅₆,3w₂₅₆), (5w₂₅₆,w₂₅₆),(5w₂₅₆,−15w₂₅₆), (5w₂₅₆,−13w₂₅₆), (5w₂₅₆,−11w₂₅₆), (5w₂₅₆,−9w₂₅₆),(5w₂₅₆,−7w₂₅₆), (5w₂₅₆,−5w₂₅₆), (5w₂₅₆,−3w₂₅₆), (5w₂₅₆,−w₂₅₆),(3w₂₅₆,15w₂₅₆), (3w₂₅₆,13w₂₅₆), (3w₂₅₆,11w₂₅₆), (3w₂₅₆,9w₂₅₆),(3w₂₅₆,7w₂₅₆), (3w₂₅₆,5w₂₅₆), (3w₂₅₆,3w₂₅₆), (3w₂₅₆,w₂₅₆),(3w₂₅₆,−15w₂₅₆), (3w₂₅₆,−13w₂₅₆), (3w₂₅₆,−11w₂₅₆), (3w₂₅₆,−9w₂₅₆),(3w₂₅₆,−7w₂₅₆), (3w₂₅₆,−5w₂₅₆), (3w₂₅₆,−3w₂₅₆), (3w₂₅₆,−w₂₅₆),(w₂₅₆,15w₂₅₆), (w₂₅₆,13w₂₅₆), (w₂₅₆,11w₂₅₆), (w₂₅₆,9w₂₅₆), (w₂₅₆,7w₂₅₆),(w₂₅₆,5w₂₅₆), (w₂₅₆,3w₂₅₆), (w₂₅₆,w₂₅₆), (w₂₅₆,−15w₂₅₆), (w₂₅₆,−13w₂₅₆),(w₂₅₆,−11w₂₅₆), (w₂₅₆,−9w₂₅₆), (w₂₅₆,−7w₂₅₆), (w₂₅₆,−5w₂₅₆),(w₂₅₆,−3w₂₅₆), (w₂₅₆,−w₂₅₆),(−15w₂₅₆,15w₂₅₆), (−15w₂₅₆,13w₂₅₆), (−15w₂₅₆,11w₂₅₆), (−15w₂₅₆,9w₂₅₆),(−15w₂₅₆,7w₂₅₆), (−15w₂₅₆,5w₂₅₆), (−15w₂₅₆,3w₂₅₆), (−15w₂₅₆,w₂₅₆),(−15w₂₅₆,−15w₂₅₆), (−15w₂₅₆,−13w₂₅₆), (−15w₂₅₆,−11w₂₅₆),(−15w₂₅₆,−9w₂₅₆), (−15w₂₅₆,−7w₂₅₆), (−15w₂₅₆,−5w₂₅₆), (−15w₂₅₆,−3w₂₅₆),(−15w₂₅₆,−w₂₅₆),(−13w₂₅₆,15w₂₅₆), (−13w₂₅₆,13w₂₅₆), (−13w₂₅₆,11w₂₅₆), (−13w₂₅₆,9w₂₅₆),(−13w₂₅₆,7w₂₅₆), (−13w₂₅₆,5w₂₅₆), (−13w₂₅₆,3w₂₅₆), (−13w₂₅₆,w₂₅₆),(−13w₂₅₆,−15w₂₅₆), (−13w₂₅₆,−13w₂₅₆), (−13w₂₅₆,−11w₂₅₆),(−13w₂₅₆,−9w₂₅₆), (−13w₂₅₆,−7w₂₅₆), (−13w₂₅₆,−5w₂₅₆), (−13w₂₅₆,−3w₂₅₆),(−13w₂₅₆,−w₂₅₆),(−11w₂₅₆,15w₂₅₆), (−11w₂₅₆,13w₂₅₆), (−11w₂₅₆,11w₂₅₆), (−11w₂₅₆,9w₂₅₆),(−11w₂₅₆,7w₂₅₆), (−11w₂₅₆,5w₂₅₆), (−11w₂₅₆,3w₂₅₆), (−11w₂₅₆,w₂₅₆),(−11w₂₅₆,−15w₂₅₆), (−11w₂₅₆,−13w₂₅₆), (−11w₂₅₆,−11w₂₅₆),(−11w₂₅₆,−9w₂₅₆), (−11w₂₅₆,−7w₂₅₆), (−11w₂₅₆,−5w₂₅₆), (−11w₂₅₆,−3w₂₅₆),(−11w₂₅₆,−w₂₅₆),(−9w₂₅₆,15w₂₅₆), (−9w₂₅₆,13w₂₅₆), (−9w₂₅₆,11w₂₅₆), (−9w₂₅₆,9w₂₅₆),(−9w₂₅₆,7w₂₅₆), (−9w₂₅₆,5w₂₅₆), (−9w₂₅₆,3w₂₅₆), (−9w₂₅₆,w₂₅₆),(−9w₂₅₆,−15w₂₅₆), (−9w₂₅₆,−13w₂₅₆), (−9w₂₅₆,−11w₂₅₆), (−9w₂₅₆,−9w₂₅₆),(−9w₂₅₆,−7w₂₅₆), (−9w₂₅₆,−5w₂₅₆), (−9w₂₅₆,−3w₂₅₆), (−9w₂₅₆,−w₂₅₆),(−7w₂₅₆,15w₂₅₆), (−7w₂₅₆,13w₂₅₆), (−7w₂₅₆,11w₂₅₆), (−7w₂₅₆,9w₂₅₆),(−7w₂₅₆,7w₂₅₆), (−7w₂₅₆,5w₂₅₆), (−7w₂₅₆,3w₂₅₆), (−7w₂₅₆,w₂₅₆),(−7w₂₅₆,−15w₂₅₆), (−7w₂₅₆,−13w₂₅₆), (−7w₂₅₆,−11w₂₅₆), (−7w₂₅₆,−9w₂₅₆),(−7w₂₅₆,−7w₂₅₆), (−7w₂₅₆,−5w₂₅₆), (−7w₂₅₆,−3w₂₅₆), (−7w₂₅₆,−w₂₅₆),(−5w₂₅₆,15w₂₅₆), (−5w₂₅₆,13w₂₅₆), (−5w₂₅₆,11w₂₅₆), (−5w₂₅₆,9w₂₅₆),(−5w₂₅₆,7w₂₅₆), (−5w₂₅₆,5w₂₅₆), (−5w₂₅₆,3w₂₅₆), (−5w₂₅₆,w₂₅₆),(−5w₂₅₆,−15w₂₅₆), (−5w₂₅₆,−13w₂₅₆), (−5w₂₅₆,−11w₂₅₆), (−5w₂₅₆,−9w₂₅₆),(−5w₂₅₆,−7w₂₅₆), (−5w₂₅₆,−5w₂₅₆), (−5w₂₅₆,−3w₂₅₆), (−5w₂₅₆,−w₂₅₆),(−3w₂₅₆,15w₂₅₆), (−3w₂₅₆,13w₂₅₆), (−3w₂₅₆,11w₂₅₆), (−3w₂₅₆,9w₂₅₆),(−3w₂₅₆,7w₂₅₆), (−3w₂₅₆,5w₂₅₆), (−3w₂₅₆,3w₂₅₆), (−3w₂₅₆,w₂₅₆),(−3w₂₅₆,−15w₂₅₆), (−3w₂₅₆,−13w₂₅₆), (−3w₂₅₆,−11w₂₅₆), (−3w₂₅₆,−9w₂₅₆),(−3w₂₅₆,−7w₂₅₆), (−3w₂₅₆,−5w₂₅₆), (−3w₂₅₆,−3w₂₅₆), (−3w₂₅₆,−w₂₅₆),(−w₂₅₆,15w₂₅₆), (−w₂₅₆,13w₂₅₆), (−w₂₅₆,11w₂₅₆), (−w₂₅₆,9w₂₅₆),(−w₂₅₆,7w₂₅₆), (−w₂₅₆,5w₂₅₆), (−w₂₅₆,3w₂₅₆), (−w₂₅₆,w₂₅₆),(−w₂₅₆,−15w₂₅₆), (−w₂₅₆,−w₂₅₆), (−w₂₅₆,−11w₂₅₆), (−w₂₅₆,−9w₂₅₆),(−w₂₅₆,−7w₂₅₆), (−w₂₅₆,−5w₂₅₆), (−w₂₅₆,−3w₂₅₆), (−w₂₅₆,−w₂₅₆).Respective coordinates of the signal points (“◯”) immediately above thevalues 00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6,and b7 in the I-Q plane serve as in-phase component I and quadraturecomponent Q of the mapped baseband signal. The relationship between theset of b0, b1, b2, b3, b4, b5, b6, and b7 (00000000 to 11111111) and thesignal point coordinates during 256QAM modulation is not limited to thatin FIG. 4 . A complex value of in-phase component I and quadraturecomponent Q of the mapped baseband signal (during 256QAM modulation)serves as a baseband signal (s₁(t) or s₂(t)).

At this point, generally average power of baseband signal 505A (s₁(t)and (s₁(i))) and average power of baseband signal 505B (s₂(t) and(s₂(i))), which are of the output of mapper 504 in FIGS. 5 to 7 , areequalized to each other. Accordingly, the following relationalexpressions hold with respect to coefficient w_(q) described in the QPSKmapping method, coefficient w₁₆ described in the 16QAM mapping method,coefficient w₆₄ described in the 64QAM mapping method, and coefficientw₂₅₆ described in the 256QAM mapping method.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 11} \right\rbrack & \; \\{w_{q} = \frac{z}{\sqrt{2}}} & ({R11}) \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 12} \right\rbrack & \; \\{w_{16} = \frac{z}{\sqrt{10}}} & ({R12}) \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 13} \right\rbrack & \; \\{w_{64} = \frac{z}{\sqrt{42}}} & ({R13}) \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 14} \right\rbrack & \; \\{w_{256} = \frac{z}{\sqrt{170}}} & ({R14})\end{matrix}$

In the DVB (Digital Video Broadcasting) standard, when modulated signals#1 and #2 are transmitted from the two antennas in the MIMO transmissionscheme, sometimes transmission average power of modulated signal #1 andtransmission average power of modulated signal #2 are set so as to bedifferent from each other. For example, Q₁≠Q₂ holds in equations (R2),(R3), (R4), (R5), and (R8).

A more specific example is considered as follows.

<1> The case that precoding matrix F (or F(i)) is given by any one ofthe following equations in equation (R2)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 15} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j0}} & {\beta \times \alpha \times e^{j0}} \\{\beta \times \alpha \times e^{j0}} & {\beta \times e^{j}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R15})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 16} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j0} & {\alpha \times e^{j0}} \\{\alpha \times e^{j0}} & e^{j}\end{pmatrix}}} & {{Formula}\mspace{14mu}({R16})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 17} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j0}} & {\beta \times \alpha \times e^{j}} \\{\beta \times \alpha \times e^{j0}} & {\beta \times e^{j0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R17})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 18} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j0} & {\alpha \times e^{j}} \\{\alpha \times e^{j0}} & e^{j0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({R18})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 19} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \alpha \times e^{j0}} & {\beta \times e^{j}} \\{\beta \times e^{j0}} & {\beta \times \alpha \times e^{j0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R19})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 20} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times e^{j0}} & e^{j} \\e^{j0} & {\alpha \times e^{j0}}\end{pmatrix}}} & {{Formula}\mspace{14mu}({R20})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 21} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \alpha \times e^{j0}} & {\beta \times e^{j0}} \\{\beta \times e^{j0}} & {\beta \times \alpha \times e^{j}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R21})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 22} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times e^{j0}} & e^{j0} \\e^{j0} & {\alpha \times e^{j}}\end{pmatrix}}} & {{Formula}\mspace{14mu}({R22})}\end{matrix}$

In equations (R15), (R16), (R17), (R18), (R19), (R20), (R21), and (R22),α may be either a real number or an imaginary number, and β may beeither a real number or an imaginary number. However, α is not 0 (zero).Also β is not 0 (zero).

or

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 23} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times {\cos\theta}} & {\beta \times {\sin\theta}} \\{\beta \times {\sin\theta}} & {{- \beta} \times {\cos\theta}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R23})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 24} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\theta} & {\sin\theta} \\{\sin\theta} & {- {\cos\theta}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R24})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 25} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times {\cos\theta}} & {{- \beta} \times {\sin\theta}} \\{\beta \times {\sin\theta}} & {\beta \times {\cos\theta}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R25})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 26} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\theta} & {- {\sin\theta}} \\{\sin\theta} & {\cos\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({R26})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 27} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times {\sin\theta}} & {{- \beta} \times {\cos\theta}} \\{\beta \times {\cos\theta}} & {\beta \times {\sin\theta}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R27})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 28} \right\rbrack & \; \\{F = \begin{pmatrix}{\sin\theta} & {- {\cos\theta}} \\{\cos\theta} & {\sin\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({R28})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 29} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times {\sin\theta}} & {\beta \times {\cos\theta}} \\{\beta \times {\cos\theta}} & {{- \beta} \times {\sin\theta}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R29})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 30} \right\rbrack & \; \\{F = \begin{pmatrix}{\sin\theta} & {\cos\theta} \\{\cos\theta} & {- {\sin\theta}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R30})}\end{matrix}$

In equations (R23), (R25), (R27), and (R29), β may be either a realnumber or an imaginary number. However, β is not 0 (zero).

or

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 30} \right\rbrack & \; \\{{F(i)} = \begin{pmatrix}{\beta \times e^{{j\theta}_{11}{(i)}}} & {\beta \times \alpha \times e^{j({{\theta_{11}{(i)}} + \lambda}}} \\{\beta \times \alpha \times e^{{j\theta}_{21}{(i)}}} & {\beta \times e^{j{({{\theta_{21}{(i)}} + \lambda + })}}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R31})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 30} \right\rbrack & \; \\{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{{j\theta}_{11}{(i)}} & {\alpha \times e^{j({{\theta_{11}{(i)}} + \lambda}}} \\{\alpha \times e^{{j\theta}_{21}{(i)}}} & e^{j{({{\theta_{21}{(i)}} + \lambda + })}}\end{pmatrix}}} & {{Formula}\mspace{14mu}({R32})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 30} \right\rbrack & \; \\{{F(i)} = \begin{pmatrix}{\beta \times \alpha \times e^{{j\theta}_{21}{(i)}}} & {\beta \times e^{j{({{\theta_{21}{(i)}} + \lambda + })}}} \\{\beta \times e^{{j\theta}_{11}{(i)}}} & {\beta \times \alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}}\end{pmatrix}} & {{Formula}\mspace{14mu}({R33})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 30} \right\rbrack & \; \\{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times e^{{j\theta}_{21}{(i)}}} & e^{j{({{\theta_{21}{(i)}} + \lambda + })}} \\e^{{j\theta}_{11}{(i)}} & {\alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}}\end{pmatrix}}} & {{Formula}\mspace{14mu}({R34})}\end{matrix}$

In the formula, θ₁₁(i) and θ₂₁(i) are a function of i (time orfrequency), λ is a fixed value, α may be either a real number or animaginary number, and β may be either a real number or an imaginarynumber. However, α is not 0 (zero). Also β is not 0 (zero).

<2> The case that precoding matrix F (or F(i)) is given by any one ofequations (15) to (30) in equation (R3)

<3> The case that precoding matrix F (or F(i)) is given by any one ofequations (15) to (30) in equation (R4)

<4> The case that precoding matrix F (or F(i)) is given by any one ofequations (15) to (34) in equation (R5)

<5> The case that precoding matrix F (or F(i)) is given by any one ofequations (15) to (30) in equation (R8)

In <1> to <5>, it is assumed that a modulation scheme for s₁(t) differsfrom a modulation scheme for s₂(t) (a modulation scheme for s₁(i)differs from a modulation scheme for s₂(i)).

Necessary points of the configuration example will be described below.The following points are necessary for the precoding methods in <1> to<5>, and can also be performed when a precoding matrix except forequations (15) to (34) is used in the precoding methods in <1> to <5>.

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number (a number of signal points in the I-Q plane, forexample, the modulation multi-level number is 16 for 16QAM) in themodulation scheme of s₁(t) (s₁(i)) (that is, baseband signal 505A) in<1> to <5>, and that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number (a number of signal points in the I-Qplane, for example, the modulation multi-level number is 64 for 64QAM)in the modulation scheme of s₂(t) (s₂(i)) (that is, baseband signal505B) in <1> to <5> (g≠h).

The g-bit data is transmitted by one symbol of s₁(t) (s₁(i)), and theh-bit data is transmitted by one symbol of s₂(t) (s₂(i)). Therefore, the(g+h) bits are transmitted in one slot constructed with one symbol ofs₁(t) (s₁(i)) and one symbol of s₂(t) (s₂(i)). At this point, thefollowing condition is required to obtain a high spatial diversity gain.

<Condition R-1>

In the case that the precoding is performed on any one of equations(R2), (R3), (R4), (R5), and (R8) (however, processing except for theprecoding is also included), the number of signal points that serve asthe candidates is 2^(g+h) in the I-Q plane for one symbol ofpost-precoding signal z₁(t) (z₁(i)). (When the signal point is producedin the I-Q plane with respect to all values that can be taken by the(g+h)-bit data for one symbol, the 2^(g+h) signal points can beproduced. The number 2^(g+h) is the number of signal points that serveas the candidates.)

Additionally, the number of signal points that serve as the candidatesis 2^(g+h) in the I-Q plane for one symbol of post-precoding signalz₂(t) (z₂(i)). (When the signal point is produced in the I-Q plane withrespect to all values that can be taken by the (g+h)-bit data for onesymbol, the 2^(g+h) signal points can be produced. The number 2^(g+h) isthe number of signal points that serve as the candidates.)

An additional condition will be described in each of equations (R2),(R3), (R4), (R5), and (R8) while <Condition R-1> is represented inanother way.

(Case 1)

The case that the processing of equation (R2) is performed using thefixed precoding matrix:

The following equation is considered as an equation in a middle stage ofa calculation of equation (R2).

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 35} \right\rbrack} & \; \\{\begin{pmatrix}{u_{1}(i)} \\{u_{2}(i)}\end{pmatrix} = {{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {{\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & {{Formula}\mspace{14mu}({R35})}\end{matrix}$

(For Case 1, precoding matrix F is set to a fixed precoding matrix(however, the precoding matrix may be switched in the case that themodulation scheme in s₁(t) (s₁(i)) and/or the modulation scheme in s₂(t)(s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when thefollowing condition holds.

<Condition R-2>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R35).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.)

Additionally, the number of signal points that serve as the candidatesis 2^(g+h) in the I-Q plane for one symbol of signal u₂t) (u₂(i)) ofequation (R35). (When the signal point is produced in the I-Q plane withrespect to all values that can be taken by the (g+h)-bit data for onesymbol, the 2^(g+h) signal points can be produced. The number 2^(g+h) isthe number of signal points that serve as the candidates.)

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R2), the following condition is considered.

<Condition R-3>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R35).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R35).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁>D₂ (D₁ is larger than D₂) holds.

FIG. 53 illustrates a relationship between the transmitting antenna andthe receiving antenna. It is assumed that modulated signal #1 (5301A) istransmitted from transmitting antenna #1 (5302A) of the transmitter, andthat modulated signal #2 (5301B) is transmitted from transmittingantenna #2 (5302B). At this point, it is assumed that z₁(t) (z₁(i))(that is, u₁(t) (u₁(i))) is transmitted from transmitting antenna #1(5302A), and that z₂(t) (z₂(i)) (that is, u₂(t) (u₂(i))) is transmittedfrom transmitting antenna #2 (5302B).

Receiving antenna #1 (5303X) and receiving antenna #2 (5303Y) of thereceiver receive the modulated signal transmitted from the transmitter(obtain received signal 530X and received signal 5304Y). At this point,it is assumed that h₁₁(t) is a propagation coefficient from transmittingantenna #1 (5302A) to receiving antenna #1 (5303X), that h₂₁(t) is apropagation coefficient from transmitting antenna #1 (5302A) toreceiving antenna #2 (5303Y), that h₁₂(t) is a propagation coefficientfrom transmitting antenna #2 (5302B) to receiving antenna #1 (5303X),and that h₂₂(t) is a propagation coefficient from transmitting antenna#2 (5302B) to receiving antenna #2 (5303Y) (t is time).

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-3> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-3′> preferably holds for |Q₁|<|Q₂|.

<Condition R-3′>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R35).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R35).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁<D₂ (D₁ is smaller than D₂) holds.

In Case 1, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 2)

The case that the processing of equation (R2) is performed using any oneof the pre-coding matrices of equations (R15) to (R30):

Equation (R35) is considered as an equation in the middle stage of thecalculation of equation (R2). For Case 2, it is assumed that precodingmatrix F is set to a fixed precoding matrix, and that precoding matrix Fis given by one of equations (R15) to (R30) (however, the precodingmatrix may be switched in the case that the modulation scheme in s₁(t)(s₁(i)) and/or the modulation scheme in s₂(t) (s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when<Condition R-2> holds.

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R2), it is considered that <Condition R-3> holdssimilarly to Case 1.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-3> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

Accordingly, when the following condition holds, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

<Condition R-3″>

P₁=P₂ holds in equation (R2) while <Condition R-3> holds.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-3″> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-3′> preferably holds for |Q₁|<|Q₂|.

For the similar reason, when the following condition holds for|Q₁|<|Q₂|, the receiver also has a higher possibility of being able toobtain the high data reception quality.

<Condition R-3′″>

P₁=P₂ holds in equation (R2) while <Condition R-3′> holds.

In Case 2, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 3)

The case that the processing of equation (R2) is performed using any oneof the pre-coding matrices of equations (R31) to (R34):

Equation (R35) is considered as an equation in the middle stage of thecalculation of equation (R2). For Case 3, it is assumed that precodingmatrix F is switched depending on the time (or frequency). It is assumedthat precoding matrix F (F(i)) is given by any one of equations (R31) to(R34).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when<Condition R-4> holds.

<Condition R-4>

When symbol number i is greater than or equal to N and less than orequal to M (N is an integer, M is an integer, and N<M (M is smaller thanN)), it is assumed that the modulation scheme of s₁(t) (s₁(i)) (that is,baseband signal 505A) is fixed (not switched), and that the modulationscheme of s₂(t) (s₂(i)) (that is, baseband signal 505B) is fixed (notswitched).

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₁(t) (u₁(i)) of equation (R35). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

Additionally, when symbol number i is greater than or equal to N andless than or equal to M, the number of candidate signal points is2^(g+h) in the I-Q plane for one symbol of signal u₂(t) (u₂(i)) ofequation (R35). (When the signal point is produced in the I-Q plane withrespect to all values that can be taken by the (g+h)-bit data for onesymbol, the 2^(g+h) signal points can be produced. The number 2^(g+h) isthe number of signal points that serve as the candidates.)

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R2), it is considered that <Condition R-5> holds.

<Condition R-5>

When symbol number i is greater than or equal to N and less than orequal to M (N is an integer, M is an integer, and N<M (M is smaller thanN)), it is assumed that the modulation scheme of s₁(t) (s₁(i)) (that is,baseband signal 505A) is fixed (not switched), and that the modulationscheme of s₂(t) (s₂(i)) (that is, baseband signal 505B) is fixed (notswitched).

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₁(t) (u₁(i)) of equation (R35). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

In symbol number i, a minimum Euclidean distance between signal pointsthat serve as 2^(g+h) candidates of u₁(t) (u₁(i)) is set to D₁(i) in theI-Q plane. (D₁(i) is a real number of 0 (zero) or more (D₁(i)≥0). In the2^(g+h) signal points, signal points located at the identical positionexist in the I-Q plane when D₁(i) is 0 (zero).)

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₂(t) (u₂(i)) of equation (R35). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

In symbol number i, a minimum Euclidean distance between signal pointsthat serve as 2^(g+h) candidates of u₂(t) (u₂(i)) is set to D₂(i) in theI-Q plane. (D₂(i) is a real number of 0 (zero) or more (D₂(i)≥0). In the2^(g+h) signal points, signal points located at the identical positionexist in the I-Q plane when D₂(i) is 0 (zero).)

At this point, D₁(i)>D₂(i) (D₁(i) is larger than D₂(i)) holds whensymbol number i is greater than or equal to N and less than or equal toM.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-5> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

Accordingly, when the following condition holds, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

<Condition R-5′>

P₁=P₂ holds in equation (R2) while <Condition R-5> holds.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-5′> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-5″> preferably holds for |Q₁|<|Q₂|.

<Condition R-5″>

When symbol number i is greater than or equal to N and less than orequal to M (N is an integer, M is an integer, and N<M (M is smaller thanN)), it is assumed that the modulation scheme of s₁(t) (s₁(i)) (that is,baseband signal 505A) is fixed (not switched), and that the modulationscheme of s₂(t) (s₂(i)) (that is, baseband signal 505B) is fixed (notswitched).

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₁(t) (u₁(i)) of equation (R35). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

In symbol number i, a minimum Euclidean distance between signal pointsthat serve as 2^(g+h) candidates of u₁(t) (u₁(i)) is set to D₁(i) in theI-Q plane. (D₁(i) is a real number of 0 (zero) or more (D₁(i)≥0). In the2^(g+h) signal points, signal points located at the identical positionexist in the I-Q plane when D₁(i) is 0 (zero).)

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₂(t) (u₂(i)) of equation (R35). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

In symbol number i, a minimum Euclidean distance between signal pointsthat serve as 2^(g+h) candidates of u₂(t) (u₂(i)) is set to D₂(i) in theI-Q plane. (D₂(i) is a real number of 0 (zero) or more (D₂(i)≥0). In the2^(g+h) signal points, signal points located at the identical positionexist in the I-Q plane when D₂(i) is 0 (zero).)

At this point, D₁(i)<D₂(i) (D₁ (i) is smaller than D₂(i)) holds whensymbol number i is greater than or equal to N and less than or equal toM.

For the similar reason, when the following condition holds for|Q₁|<|Q₂|, the receiver also has a higher possibility of being able toobtain the high data reception quality.

<Condition R-5′″>

P₁=P₂ holds in equation (R2) while <Condition R-5″> holds.

In Case 3, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 4)

The case that the processing of equation (R3) is performed using thefixed pre-coding matrix:

The following equation is considered as an equation in a middle stage ofa calculation of equation (R3).

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 36} \right\rbrack} & \; \\{\begin{pmatrix}{u_{1}(i)} \\{u_{2}(i)}\end{pmatrix} = {{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {{\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & {{Formula}\mspace{14mu}({R36})}\end{matrix}$

(For Case 4, precoding matrix F is set to a fixed precoding matrix(however, the precoding matrix may be switched in the case that themodulation scheme in s₁(t) (s₁(i)) and/or the modulation scheme in s₂(t)(s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when thefollowing condition holds.

<Condition R-6>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R36).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.)

Additionally, the number of signal points that serve as the candidatesis 2^(g+h) in the I-Q plane for one symbol of signal u₂(t) (u₂(i)) ofequation (R36). (When the signal point is produced in the I-Q plane withrespect to all values that can be taken by the (g+h)-bit data for onesymbol, the 2^(g+h) signal points can be produced. The number 2^(g+h) isthe number of signal points that serve as the candidates.)

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R3), the following condition is considered.

<Condition R-7>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R36).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R36).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁>D₂ (D₁ is larger than D₂) holds.

FIG. 53 illustrates a relationship between the transmitting antenna andthe receiving antenna. It is assumed that modulated signal #1 (5301A) istransmitted from transmitting antenna #1 (5302A) of the transmitter, andthat modulated signal #2 (5301B) is transmitted from transmittingantenna #2 (5302B). At this point, it is assumed that z₁(t) (z₁(i))(that is, u₁(t) (u₁(i))) is transmitted from transmitting antenna #1(5302A), and that z₂(t) (z₂(i)) (that is, u₂(t) (u₂(i))) is transmittedfrom transmitting antenna #2 (5302B).

Receiving antenna #1 (5303X) and receiving antenna #2 (5303Y) of thereceiver receive the modulated signal transmitted from the transmitter(obtain received signal 530X and received signal 5304Y). At this point,it is assumed that h₁₁(t) is a propagation coefficient from transmittingantenna #1 (5302A) to receiving antenna #1 (5303X), that h₂₁(t) is apropagation coefficient from transmitting antenna #1 (5302A) toreceiving antenna #2 (5303Y), that h₁₂(t) is a propagation coefficientfrom transmitting antenna #2 (5302B) to receiving antenna #1 (5303X),and that h₂₂(t) is a propagation coefficient from transmitting antenna#2 (5302B) to receiving antenna #2 (5303Y) (t is time).

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-7> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-7′> preferably holds for |Q₁|<|Q₂|.

<Condition R-7′>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R36).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R36).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁<D₂ (D₁ is smaller than D₂) holds.

In Case 4, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 5)

The case that the processing of equation (R3) is performed using any oneof the precoding matrices of equations (R15) to (R30):

Equation (R36) is considered as an equation in the middle stage of thecalculation of equation (R3). For Case 5, it is assumed that precodingmatrix F is set to a fixed precoding matrix, and that precoding matrix Fis given by one of equations (R15) to (R30) (however, the precodingmatrix may be switched in the case that the modulation scheme in s₁(t)(s₁(i)) and/or the modulation scheme in s₂(t) (s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when<Condition R-6> holds.

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R3), it is considered that <Condition R-7> holdssimilarly to Case 4.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-7> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

Accordingly, when the following condition holds, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

<Condition R-7″>

P₁=P₂ holds in equation (R3) while <Condition R-7> holds.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-7″> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-7′> preferably holds for |Q₁|<|Q₂|.

For the similar reason, when the following condition holds for|Q₁|<|Q₂|, the receiver also has a higher possibility of being able toobtain the high data reception quality.

<Condition R-7′″>

P₁=P₂ holds in equation (R3) while <Condition R-7′> holds.

In Case 5, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 6)

The case that the processing of equation (R4) is performed using thefixed pre-coding matrix:

The following equation is considered as an equation in a middle stage ofa calculation of equation (R4).

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 37} \right\rbrack & \; \\{\begin{pmatrix}{u_{1}(i)} \\{u_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} = {{\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & \left( {R\mspace{14mu} 3\mspace{11mu} 7} \right)\end{matrix}$

(For Case 6, precoding matrix F is set to a fixed precoding matrix(however, the precoding matrix may be switched in the case that themodulation scheme in s₁(t) (s₁(i)) and/or the modulation scheme in s₂(t)(s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when thefollowing condition holds.

<Condition R-8>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R37).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.)

Additionally, the number of signal points that serve as the candidatesis 2^(g+h) in the I-Q plane for one symbol of signal u₂(t) (u₂(i)) ofequation (R37). (When the signal point is produced in the I-Q plane withrespect to all values that can be taken by the (g+h)-bit data for onesymbol, the 2^(g+h) signal points can be produced. The number 2^(g+h) isthe number of signal points that serve as the candidates.)

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R4), the following condition is considered.

<Condition R-9>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R37).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R37).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁>D₂ (D₁ is larger than D₂) holds.

FIG. 53 illustrates a relationship between the transmitting antenna andthe receiving antenna. It is assumed that modulated signal #1 (5301A) istransmitted from transmitting antenna #1 (5302A) of the transmitter, andthat modulated signal #2 (5301B) is transmitted from transmittingantenna #2 (5302B). At this point, it is assumed that z₁(t) (z₁(i))(that is, u₁(t) (u₁(i))) is transmitted from transmitting antenna #1(5302A), and that z₂(t) (z₂(i)) (that is, u₂(t) (u₂(i))) is transmittedfrom transmitting antenna #2 (5302B).

Receiving antenna #1 (5303X) and receiving antenna #2 (5303Y) of thereceiver receive the modulated signal transmitted from the transmitter(obtain received signal 530X and received signal 5304Y). At this point,it is assumed that h₁₁(t) is a propagation coefficient from transmittingantenna #1 (5302A) to receiving antenna #1 (5303X), that h₂₁(t) is apropagation coefficient from transmitting antenna #1 (5302A) toreceiving antenna #2 (5303Y), that h₁₂(t) is a propagation coefficientfrom transmitting antenna #2 (5302B) to receiving antenna #1 (5303X),and that h₂₂(t) is a propagation coefficient from transmitting antenna#2 (5302B) to receiving antenna #2 (5303Y) (t is time).

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-9> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-9′> preferably holds for |Q₁|<|Q₂|.

<Condition R-9′>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R37).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R37).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁<D₂ (D₁ is smaller than D₂) holds.

In Case 6, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 7)

The case that the processing of equation (R4) is performed using any oneof the precoding matrices of equations (R15) to (R30):

Equation (R37) is considered as an equation in the middle stage of thecalculation of equation (R4). For Case 7, it is assumed that precodingmatrix F is set to a fixed precoding matrix, and that precoding matrix Fis given by one of equations (R15) to (R30) (however, the precodingmatrix may be switched in the case that the modulation scheme in s₁(t)(s₁(i)) and/or the modulation scheme in s₂(t) (s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when<Condition R-8> holds.

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R4), it is considered that <Condition R-9> holdssimilarly to Case 6.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-9> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

Accordingly, when the following condition holds, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

<Condition R-9″>

P₁=P₂ holds in equation (R4) while <Condition R-9> holds.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-9″> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-9′> preferably holds for |Q₁|<|Q₂|.

For the similar reason, when the following condition holds for|Q₁|<|Q₂|, the receiver also has a higher possibility of being able toobtain the high data reception quality.

<Condition R-9′″>

P₁=P₂ holds in equation (R4) while <Condition R-9′> holds.

In Case 7, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 8)

The case that the processing of equation (R5) is performed using thefixed pre-coding matrix:

The following equation is considered as an equation in a middle stage ofa calculation of equation (R5).

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 38} \right\rbrack & \; \\{\begin{pmatrix}{u_{1}(i)} \\{u_{2}(i)}\end{pmatrix} = {{F\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & {{Formula}\mspace{14mu}({R38})}\end{matrix}$

(For Case 8, precoding matrix F is set to a fixed precoding matrix(however, the precoding matrix may be switched in the case that themodulation scheme in s₁(t) (s₁(i)) and/or the modulation scheme in s₂(t)(s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when thefollowing condition holds.

<Condition R-10>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R38).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.)

Additionally, the number of signal points that serve as the candidatesis 2^(g+h) in the I-Q plane for one symbol of signal u₂(t) (u₂(i)) ofequation (R38). (When the signal point is produced in the I-Q plane withrespect to all values that can be taken by the (g+h)-bit data for onesymbol, the 2^(g+h) signal points can be produced. The number 2^(g+h) isthe number of signal points that serve as the candidates.)

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R5), the following condition is considered.

<Condition R-11>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R38).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R38).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁> D₂ (D₁ is larger than D₂) holds.

FIG. 53 illustrates a relationship between the transmitting antenna andthe receiving antenna. It is assumed that modulated signal #1 (5301A) istransmitted from transmitting antenna #1 (5302A) of the transmitter, andthat modulated signal #2 (5301B) is transmitted from transmittingantenna #2 (5302B). At this point, it is assumed that z₁(t) (z₁(i))(that is, u₁(t) (u₁(i))) is transmitted from transmitting antenna #1(5302A), and that z₂(t) (z₂(i)) (that is, u₂(t) (u₂(i))) is transmittedfrom transmitting antenna #2 (5302B).

Receiving antenna #1 (5303X) and receiving antenna #2 (5303Y) of thereceiver receive the modulated signal transmitted from the transmitter(obtain received signal 530X and received signal 5304Y). At this point,it is assumed that h₁₁(t) is a propagation coefficient from transmittingantenna #1 (5302A) to receiving antenna #1 (5303X), that h₂₁(t) is apropagation coefficient from transmitting antenna #1 (5302A) toreceiving antenna #2 (5303Y), that h₁₂(t) is a propagation coefficientfrom transmitting antenna #2 (5302B) to receiving antenna #1 (5303X),and that h₂₂(t) is a propagation coefficient from transmitting antenna#2 (5302B) to receiving antenna #2 (5303Y) (t is time).

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-11> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-11> preferably holds for |Q₁|<|Q₂|.

<Condition R-11′>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R38).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R38).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁<D₂ (D₁ is smaller than D₂) holds.

In Case 8, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 9)

The case that the processing of equation (R5) is performed using any oneof the pre-coding matrices of equations (R15) to (R30):

Equation (R38) is considered as an equation in the middle stage of thecalculation of equation (R5). For Case 9, it is assumed that precodingmatrix F is set to a fixed precoding matrix, and that precoding matrix Fis given by one of equations (R15) to (R30) (however, the precodingmatrix may be switched in the case that the modulation scheme in s₁(t)(s₁(i)) and/or the modulation scheme in s₂(t) (s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when<Condition R-10> holds.

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R5), it is considered that <Condition R-11> holdssimilarly to Case 8.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-11> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-11′> preferably holds for|Q₁|<|Q₂|.

In Case 9, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 10)

The case that the processing of equation (R5) is performed using any oneof the pre-coding matrices of equations (R31) to (R34):

Equation (R38) is considered as an equation in the middle stage of thecalculation of equation (R5). For Case 10, it is assumed that precodingmatrix F is switched depending on the time (or frequency). It is assumedthat precoding matrix F (F(i)) is given by any one of equations (R31) to(R34).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when<Condition R-12> holds.

<Condition R-12>

When symbol number i is greater than or equal to N and less than orequal to M (N is an integer, M is an integer, and N<M (M is smaller thanN)), it is assumed that the modulation scheme of s₁(t) (s₁(i)) (that is,baseband signal 505A) is fixed (not switched), and that the modulationscheme of s₂(t) (s₂(i)) (that is, baseband signal 505B) is fixed (notswitched).

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₁(t) (u₁(i)) of equation (R38). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

Additionally, when symbol number i is greater than or equal to N andless than or equal to M, the number of candidate signal points is2^(g+h) in the I-Q plane for one symbol of signal u₂(t) (u₂(i)) ofequation (R38). (When the signal point is produced in the I-Q plane withrespect to all values that can be taken by the (g+h)-bit data for onesymbol, the 2^(g+h) signal points can be produced. The number 2^(g+h) isthe number of signal points that serve as the candidates.)

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R5), it is considered that <Condition R-13> holds.

<Condition R-13>

When symbol number i is greater than or equal to N and less than orequal to M (N is an integer, M is an integer, and N<M (M is smaller thanN)), it is assumed that the modulation scheme of s₁(t) (s₁(i)) (that is,baseband signal 505A) is fixed (not switched), and that the modulationscheme of s₂(t) (s₂(i)) (that is, baseband signal 505B) is fixed (notswitched).

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₁(t) (u₁(i)) of equation (R38). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

In symbol number i, a minimum Euclidean distance between signal pointsthat serve as 2^(g+h) candidates of u₁(t) (u₁(i)) is set to D₁(i) in theI-Q plane. (D₁(i) is a real number of 0 (zero) or more (D₁(i)≥0). In the2^(g+h) signal points, signal points located at the identical positionexist in the I-Q plane when D₁(i) is 0 (zero).)

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₂(t) (u₂(i)) of equation (R38). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

In symbol number i, a minimum Euclidean distance between signal pointsthat serve as 2^(g+h) candidates of u₂(t) (u₂(i)) is set to D₂(i) in theI-Q plane. (D₂(i) is a real number of 0 (zero) or more (D₂(i)≥0). In the2^(g+h) signal points, signal points located at the identical positionexist in the I-Q plane when D₂(i) is 0 (zero).)

At this point, D₁(i)>D₂(i) (D₁(i) is larger than D₂(i)) holds whensymbol number i is greater than or equal to N and less than or equal toM.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-13> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

Accordingly, when the following condition holds, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-13″> preferably holds for|Q₁|<|Q₂|.

<Condition R-13″>

When symbol number i is greater than or equal to N and less than orequal to M (N is an integer, M is an integer, and N<M (M is smaller thanN)), it is assumed that the modulation scheme of s₁(t) (s₁(i)) (that is,baseband signal 505A) is fixed (not switched), and that the modulationscheme of s₂(t) (s₂(i)) (that is, baseband signal 505B) is fixed (notswitched).

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₁(t) (u₁(i)) of equation (R38). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

In symbol number i, a minimum Euclidean distance between signal pointsthat serve as 2^(g+h) candidates of u₁(t) (u₁(i)) is set to D₁(i) in theI-Q plane. (D₁(i) is a real number of 0 (zero) or more (D₁(i)≥0). In the2^(g+h) signal points, signal points located at the identical positionexist in the I-Q plane when D₁(i) is 0 (zero).)

When symbol number i is greater than or equal to N and less than orequal to M, the number of candidate signal points is 2^(g+h) in the I-Qplane for one symbol of signal u₂(t) (u₂(i)) of equation (R38). (Whenthe signal point is produced in the I-Q plane with respect to all valuesthat can be taken by the (g+h)-bit data for one symbol, the 2^(g+h)signal points can be produced. The number 2^(g+h) is the number ofsignal points that serve as the candidates.)

In symbol number i, a minimum Euclidean distance between signal pointsthat serve as 2^(g+h) candidates of u₂(t) (u₂(i)) is set to D₂(i) in theI-Q plane. (D₂(i) is a real number of 0 (zero) or more (D₂(i)≥0). In the2^(g+h) signal points, signal points located at the identical positionexist in the I-Q plane when D₂(i) is 0 (zero).)

At this point, D₁(i)<D₂(i) (D₁(i) is smaller than D₂(i)) holds whensymbol number i is greater than or equal to N and less than or equal toM.

In Case 10, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 11)

The case that the processing of equation (R8) is performed using thefixed pre-coding matrix:

The following equation is considered as an equation in a middle stage ofa calculation of equation (R8).

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 39} \right\rbrack & \; \\{\begin{pmatrix}{u_{1}(i)} \\{u_{2}(i)}\end{pmatrix} = {{F\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & {{Formula}\mspace{14mu}({R39})}\end{matrix}$

(For Case 11, precoding matrix F is set to a fixed precoding matrix(however, the precoding matrix may be switched in the case that themodulation scheme in s₁(t) (s₁(i)) and/or the modulation scheme in s₂(t)(s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when thefollowing condition holds.

<Condition R-14>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R39).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.)

Additionally, the number of signal points that serve as the candidatesis 2^(g+h) in the I-Q plane for one symbol of signal u₂(t) (u₂(i)) ofequation (R39). (When the signal point is produced in the I-Q plane withrespect to all values that can be taken by the (g+h)-bit data for onesymbol, the 2^(g+h) signal points can be produced. The number 2^(g+h) isthe number of signal points that serve as the candidates.)

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R8), the following condition is considered.

<Condition R-15>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R39).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R39).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁>D₂ (D₁ is larger than D₂) holds.

FIG. 53 illustrates a relationship between the transmitting antenna andthe receiving antenna. It is assumed that modulated signal #1 (5301A) istransmitted from transmitting antenna #1 (5302A) of the transmitter, andthat modulated signal #2 (5301B) is transmitted from transmittingantenna #2 (5302B). At this point, it is assumed that z₁(t) (z₁(i))(that is, u₁(t) (u₁(i))) is transmitted from transmitting antenna #1(5302A), and that z₂(t) (z₂(i)) (that is, u₂(t) (u₂(i))) is transmittedfrom transmitting antenna #2 (5302B).

Receiving antenna #1 (5303X) and receiving antenna #2 (5303Y) of thereceiver receive the modulated signal transmitted from the transmitter(obtain received signal 530X and received signal 5304Y). At this point,it is assumed that h₁₁(t) is a propagation coefficient from transmittingantenna #1 (5302A) to receiving antenna #1 (5303X), that h₂₁(t) is apropagation coefficient from transmitting antenna #1 (5302A) toreceiving antenna #2 (5303Y), that h₁₂(t) is a propagation coefficientfrom transmitting antenna #2 (5302B) to receiving antenna #1 (5303X),and that h₂₂(t) is a propagation coefficient from transmitting antenna#2 (5302B) to receiving antenna #2 (5303Y) (t is time).

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-15> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-15′> preferably holds for|Q₁|<|Q₂|.

<Condition R-15′>

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₁(t) (u₁(i)) of equation (R39).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₁(t)(u₁(i)) is set to D₁ in the I-Q plane. (D₁ is a real number of 0 (zero)or more (D₁≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₁ is 0 (zero).)

The number of signal points that serve as the candidates is 2^(g+h) inthe I-Q plane for one symbol of signal u₂(t) (u₂(i)) of equation (R39).(When the signal point is produced in the I-Q plane with respect to allvalues that can be taken by the (g+h)-bit data for one symbol, the2^(g+h) signal points can be produced. The number 2^(g+h) is the numberof signal points that serve as the candidates.) A minimum Euclideandistance between signal points that serve as 2^(g+h) candidates of u₂(t)(u₂(i)) is set to D₂ in the I-Q plane. (D₂ is a real number of 0 (zero)or more (D₂≥0). In the 2^(g+h) signal points, signal points located atthe identical position exist in the I-Q plane when D₂ is 0 (zero).)

At this point, D₁<D₂ (D₁ is smaller than D₂) holds.

In Case 11, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

(Case 12)

The case that the processing of equation (R8) is performed using any oneof the pre-coding matrices of equations (R15) to (R30):

Equation (R39) is considered as an equation in the middle stage of thecalculation of equation (R8). For Case 12, it is assumed that precodingmatrix F is set to a fixed precoding matrix, and that precoding matrix Fis given by one of equations (R15) to (R30) (however, the precodingmatrix may be switched in the case that the modulation scheme in s₁(t)(s₁(i)) and/or the modulation scheme in s₂(t) (s₂(i)) are switched).

It is assumed that 2^(g) (g is an integer of 1 or more) is a modulationmulti-level number of the modulation scheme in s₁(t) (s₁(i)) (that is,baseband signal 505A), that 2^(h) (h is an integer of 1 or more) is amodulation multi-level number of the modulation scheme in s₂(t) (s₂(i))(that is, baseband signal 505B), and that g is not equal to h.

At this point, the high spatial diversity gain can be obtained when<Condition R-14> holds.

For |Q₁|>|Q₂| (an absolute value of Q₁ is larger than an absolute valueof Q₂) in equation (R8), it is considered that <Condition R-15> holdssimilarly to Case 11.

At this point, because |Q₁|>|Q₂| holds, there is a possibility that areception state of the modulated signal of z₁(t) (z₁(i)) (that is, u₁(t)(u₁(i))) is a dominant factor of reception quality of the received data.Accordingly, when <Condition R-15> is satisfied, the receiver has ahigher possibility of being able to obtain the high data receptionquality.

For the similar reason, <Condition R-15′> preferably holds for|Q₁|<|Q₂|.

In Case 12, for example, QPSK, 16QAM, 64QAM, and 256QAM are applied asthe modulation scheme in s₁(t) (s₁(i)) and the modulation scheme ins₂(t) (s₂(i)) as described above. At this point, the specific mappingmethod is described in the above configuration example. Alternatively, amodulation scheme except for QPSK, 16QAM, 64QAM, and 256QAM may be used.

As described above in the configuration examples, in the transmissionmethod for transmitting the two post-precoding modulated signals fromthe different antennas, the minimum Euclidean distance between thesignal points of the modulated signal having the larger averagetransmission power is increased in the I-Q plane, which allows thereceiver to have the high possibility of being able to obtain the highdata reception quality.

Each of the transmitting antenna and receiving antenna in theconfiguration examples may be constructed with a plurality of antennas.The different antennas that transmit the two post-precoding modulatedsignals may be used so as to simultaneously transmit one modulatedsignal at different times.

The above precoding method can also be performed when the single-carrierscheme, the OFDM scheme, the multi-carrier scheme such as the OFDMscheme in which a wavelet transformation is used, and a spread spectrumscheme are applied.

Specific examples of exemplary embodiments are described later indetail, and operation of the receiver is also described later.

Configuration Example S1

In configuration example S1, a more specific example of the precodingmethod in the case that the two transmitted signals of configurationexample R1 differ from each other in the transmission average powerswill be described below.

FIG. 5 illustrates a configuration example of a portion that generates amodulated signal when the transmitter of a base station (such as abroadcasting station and an access point) can change a transmissionscheme.

The transmitter of the base station (such as the broadcasting stationand the access point) will be described below with reference to FIG. 5 .

In FIG. 5 , information 501 and control signal 512 are input to encoder502, and encoder 502 performs coding based on information about a codingrate and a code length (block length) included in control signal 512,and outputs coded data 503.

Coded data 503 and control signal 512 are input to mapper 504. It isassumed that control signal 512 assigns the transmission of the twostreams as a transmission scheme. Additionally, it is assumed thatcontrol signal 512 assigns modulation scheme α and modulation scheme βas respective modulation schemes of the two streams. It is assumed thatmodulation scheme α is a modulation scheme for modulating x-bit data,and that modulation scheme β is a modulation scheme for modulating y-bitdata (for example, a modulation scheme for modulating 4-bit data for16QAM (16 Quadrature Amplitude Modulation), and a modulation scheme formodulating 6-bit data for 64QAM (64 Quadrature Amplitude Modulation)).

Mapper 504 modulates the x-bit data in (x+y)-bit data using modulationscheme α to generate and output baseband signal s₁(t) (505A), andmodulates the remaining y-bit data using modulation scheme β to outputbaseband signal s₂(t) (505B). (One mapper is provided in FIG. 5 .Alternatively, a mapper that generates baseband signal s₁(t) and amapper that generates baseband signal s₂(t) may separately be provided.At this point, coded data 503 is divided in the mapper that generatesbaseband signal s₁(t) and the mapper that generates baseband signals₂(t).)

Each of s₁(t) and s₂(t) is represented as a complex number (however, maybe one of a complex number and a real number), and t is time. For thetransmission scheme in which multi-carrier such as OFDM (OrthogonalFrequency Division Multiplexing) is used, it can also be considered thats₁ and s₂ are a function of frequency f like s₁(f) and s₂(f) or that s₁and s₂ are a function of time t and frequency f like s₁(t,f) ands₂(t,f).

Hereinafter, the baseband signal, a precoding matrix, a phase change,and the like are described as the function of time t. Alternatively, thebaseband signal, the precoding matrix, the phase change, and the likemay be considered to be the function of frequency f or the function oftime t and frequency f.

Accordingly, sometimes the baseband signal, the precoding matrix, thephase change, and the like are described as a function of symbol numberi. In this case, the baseband signal, the precoding matrix, the phasechange, and the like may be considered to be the function of time t, thefunction of frequency f, or the function of time t and frequency f. Thatis, the symbol and the baseband signal may be generated and disposed ineither a time-axis direction or a frequency-axis direction. The symboland the baseband signal may be generated and disposed in the time-axisdirection and the frequency-axis direction.

Baseband signal s₁(t) (505A) and control signal 512 are input to powerchanger 506A (power adjuster 506A), and power changer 506A (poweradjuster 506A) sets real number P₁ based on control signal 512, andoutputs (P₁×s₁(t)) as power-changed signal 507A (P₁ may be a complexnumber).

Similarly, baseband signal s₂(t) (505B) and control signal 512 are inputto power changer 506B (power adjuster 506B), and power changer 506B(power adjuster 506B) sets real number P₂, and outputs (P₂×s₂(t)) aspower-changed signal 507B (P₂ may be a complex number).

Power-changed signal 507A, power-changed signal 507B, and control signal512 are input to weighting synthesizer 508, and weighting synthesizer508 sets precoding matrix F (or F(i)) based on control signal 512.Assuming that i is a slot number (symbol number), weighting synthesizer508 performs the following calculation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 40} \right\rbrack & \; \\{\begin{pmatrix}{u_{1}(i)} \\{u_{2}(i)}\end{pmatrix} = {{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {{\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & \left( {S\mspace{14mu} 1} \right)\end{matrix}$

In the formula, each of a(i), b(i), c(i), and d(i) is represented as acomplex number (may be represented as a real number), and at least threeof a(i), b(i), c(i), and d(i) must not be 0 (zero). The precoding matrixmay be a function of i or does not need to be the function of i. Whenthe precoding matrix is the function of i, the precoding matrix isswitched by a slot number (symbol number).

Weighting synthesizer 508 outputs u₁(i) in equation (S1) asweighting-synthesized signal 509A, and outputs u₂(i) in equation (S1) asweighting-synthesized signal 509B.

Weighting-synthesized signal 509A (u₁(i)) and control signal 512 areinput to power changer 510A, and power changer 510A sets real number Q₁based on control signal 512, and outputs (Q₁(Q₁ is a real number)×u₁(t))as power-changed signal 511A (z₁(i)) (alternatively, Q₁ may be a complexnumber).

Similarly, weighting-synthesized signal 509B (u₂(i)) and control signal512 are input to power changer 510B, and power changer 510B sets realnumber Q₂ based on control signal 512, and outputs (Q₂ (Q₂ is a realnumber)×u₂(t)) as power-changed signal 511A (z₂(i)) (alternatively, Q₂may be a complex number).

Accordingly, the following equation holds.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 41} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{s}(i)}}\end{pmatrix}} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & \left( {S\mspace{14mu} 2} \right)\end{matrix}$

The transmission method in the case that two streams different fromthose in FIG. 5 will be described with reference to FIG. 6 . In FIG. 6 ,the component similar to that in FIG. 5 is designated by the identicalreference mark.

Signal 509B in which u₂(i) in equation (S1) is weighting-synthesized andcontrol signal 512 are input to phase changer 601, and phase changer 601changes a phase of signal 509B in which u₂(i) in equation (S1) isweighting-synthesized based on control signal 512. Accordingly, thesignal in which the phase of signal 509B in which u₂(i) in equation (S1)is weighting-synthesized is represented as (e^(jθ(i))×u₂(i)), and phasechanger 601 outputs (e^(jθ(i))×u₂(i)) as phase-changed signal 602 (j isan imaginary unit). The changed phase constitutes a characteristicportion that the changed phase is the function of i like θ(i).

Each of power changers 510A and 510B in FIG. 6 changes power of theinput signal. Accordingly, outputs z₁(i) and z₂(i) of power changers510A and 510B in FIG. 6 are given by the following equation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 42} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{s}(i)}}\end{pmatrix}} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & \left( {S\mspace{14mu} 3} \right)\end{matrix}$

FIG. 7 illustrates the configuration different from that in FIG. 6 asthe method for performing equation (S3). A difference between theconfigurations in FIGS. 6 and 7 is that the positions of the powerchanger and phase changer are exchanged (the function of changing thepower and the function of changing the phase are not changed). At thispoint, z₁(i) and z₂(i) are given by the following equation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 43} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} = {{\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{s}(i)}}\end{pmatrix}} = {\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & \left( {S\mspace{14mu} 4} \right)\end{matrix}$

z₁(i) in equation (S3) is equal to z₁(i) in equation (S4), and z₂(i) inequation (S3) is equal to z₂(i) in equation (S4).

As to phase value θ(i) to be changed in equations (S3) and (S4),assuming that (θ(i+1)−θ(i)) is set to a fixed value, there is a highpossibility that the receiver obtains the good data reception quality ina radio wave propagation environment where a direct wave is dominant.However, a method for providing phase value θ(i) to be changed is notlimited to the above example.

FIG. 8 illustrates a configuration example of a signal processor thatprocesses signals z₁(i) and z₂(i) obtained in FIGS. 5 to 7 .

Signal z₁(i) (801A), pilot symbol 802A, control information symbol 803A,and control signal 512 are input to inserter 804A, and inserter 804Ainserts pilot symbol 802A and control information symbol 803A in signal(symbol) z₁(i) (801A) according to a frame configuration included incontrol signal 512, and outputs modulated signal 805A according to theframe configuration.

Pilot symbol 802A and control information symbol 803A are a symbolmodulated using BPSK (Binary Phase Shift Keying), QPSK (Quadrature PhaseShift Keying), and the like (other modulation schemes may be used).

Modulated signal 805A and control signal 512 are input to radio section806A, and radio section 806A performs pieces of processing such asfrequency conversion and amplification on modulated signal 805A based oncontrol signal 512 (performs inverse Fourier transform when the OFDMscheme is used), and outputs transmitted signal 807A as a radio wavefrom antenna 808A.

Signal z₂(i) (801B), pilot symbol 802B, control information symbol 803B,and control signal 512 are input to inserter 804B, and inserter 804Binserts pilot symbol 802B and control information symbol 803B in signal(symbol) z₂(i) (801B) according to the frame configuration included incontrol signal 512, and outputs modulated signal 805B according to theframe configuration.

Pilot symbol 802B and control information symbol 803B are a symbolmodulated using BPSK (Binary Phase Shift Keying), QPSK (Quadrature PhaseShift Keying), and the like (other modulation schemes may be used).

Modulated signal 805B and control signal 512 are input to radio section806B, and radio section 806B performs the pieces of processing such asthe frequency conversion and the amplification on modulated signal 805Bbased on control signal 512 (performs the inverse Fourier transform whenthe OFDM scheme is used), and outputs transmitted signal 807B as a radiowave from antenna 808B.

Signals z₁(i) (801A) and z₂(i) (801B) having the identical number of iare transmitted from different antennas at the identical time and theidentical (common) frequency (that is, the transmission method in whichthe MIMO scheme is used).

Pilot symbols 802A and 802B are a symbol that is used when the receiverperforms the signal detection, the estimation of the frequency offset,gain control, the channel estimation, and the like. Although the symbolis named the pilot symbol in this case, the symbol may be named othernames such as a reference symbol.

Control information symbols 803A and 803B are a symbol that transmitsthe information about the modulation scheme used in the transmitter, theinformation about the transmission scheme, the information about theprecoding scheme, the information about an error correction code scheme,the information about the coding rate of an error correction code, andthe information about a block length (code length) of the errorcorrection code to the receiver. The control information symbol may betransmitted using only one of control information symbols 803A and 803B.

FIG. 9 illustrates an example of the frame configuration attime-frequency when the two streams are transmitted. In FIG. 9 , ahorizontal axis indicates a frequency, a vertical axis indicates time.FIG. 9 illustrates a configuration of the symbol from carriers 1 to 38from clock time $1 to clock time $11.

FIG. 9 simultaneously illustrates the frame configuration of thetransmitted signal transmitted from antenna 808A in FIG. 8 and the frameof the transmitted signal transmitted from antenna 808B in FIG. 8 .

In FIG. 9 , a data symbol corresponds to signal (symbol) z₁(i) for theframe of the transmitted signal transmitted from antenna 808A in FIG. 8. The pilot symbol corresponds to pilot symbol 802A.

In FIG. 9 , a data symbol corresponds to signal (symbol) z₂(i) for theframe of the transmitted signal transmitted from antenna 808B in FIG. 8. The pilot symbol corresponds to pilot symbol 802B.

Accordingly, as described above, signals z₁(i) (801A) and z₂(i) (801B)having the identical number of i are transmitted from different antennasat the identical time and the identical (common) frequency. Theconfiguration of the pilot symbol is not limited to that in FIG. 9 . Forexample, a time interval and a frequency interval of the pilot symbolare not limited to those in FIG. 9 . In FIG. 9 , the pilot symbols aretransmitted at the identical clock time and the identical frequency(identical (sub-) carrier) from antennas 808A and 808B in FIG. 8 .Alternatively, for example, the pilot symbol may be disposed in notantenna 808B in FIG. 8 but antenna 808A in FIG. 8 at time A andfrequency a ((sub-) carrier a), and the pilot symbol may be disposed innot antenna 808A in FIG. 8 but antenna 808B in FIG. 8 at time B andfrequency b ((sub-) carrier b).

Although only the data symbol and the pilot symbol are illustrated inFIG. 9 , other symbols such as a control information symbol may beincluded in the frame.

Although the case that a part (or whole) of the power changer exists isdescribed with reference to FIGS. 5 to 7 , it is also considered that apart of the power changer is missing.

For example, in the case that power changer 506A (power adjuster 506A)and power changer 506B (power adjuster 506B) do not exist in FIG. 5 ,z₁(i) and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 44} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & \left( {S\mspace{14mu} 5} \right)\end{matrix}$

In the case that power changer 510A (power adjuster 510A) and powerchanger 510B (power adjuster 510B) do not exist in FIG. 5 , z₁(i) andz₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 45} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & \left( {S\mspace{14mu} 6} \right)\end{matrix}$

In the case that power changer 506A (power adjuster 506A), power changer506B (power adjuster 506B), power changer 510A (power adjuster 510A),and power changer 510B (power adjuster 510B) do not exist in FIG. 5 ,z₁(i) and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 46} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & \left( {S\mspace{14mu} 7} \right)\end{matrix}$

In the case that power changer 506A (power adjuster 506A) and powerchanger 506B (power adjuster 506B) do not exist in FIG. 6 or 7 , z₁(i)and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 47} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & \left( {S\mspace{14mu} 8} \right)\end{matrix}$

In the case that power changer 510A (power adjuster 510A) and powerchanger 510B (power adjuster 510B) do not exist in FIG. 6 or 7 , z₁(i)and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 48} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & \left( {S\mspace{14mu} 9} \right)\end{matrix}$

In the case that power changer 506A (power adjuster 506A), power changer506B (power adjuster 506B), power changer 510A (power adjuster 510A),and power changer 510B (power adjuster 510B) do not exist in FIG. 6 or 7, z₁(i) and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 49} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & \left( {S\mspace{14mu} 1\mspace{11mu} 0} \right)\end{matrix}$

A more specific example of the precoding method in the case that the twotransmitted signals of configuration example R1 differ from each otherin the transmission average powers during the adoption of the (MIMO(Multiple Input Multiple Output) scheme) transmission method fortransmitting the two streams will be described below.

Example 1

In mapper 504 of FIGS. 5 to 7 , the modulation scheme for obtainings₁(t) (s₁(i)) is set to 16QAM while the modulation scheme for obtainings₂(t) (s₂(i)) is set to 64QAM. An example of conditions associated withthe configuration and power change of precoding matrix (F) when theprecoding and/or the power change is performed on, for example, one ofequations (s2), (S3), (S4), (S5), and (S8) will be described below.

The 16QAM mapping method will be described below. FIG. 10 illustrates anarrangement example of 16QAM signal points in the I-Q plane. In FIG. 10, 16 marks “◯” indicate 16QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 16 signal points included in 16QAM (indicated by themarks “◯” in FIG. 10 ) are obtained as follows. (w₁₆ is a real numberlarger than 0)

(3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆), (3w₁₆,−3w₁₆), (w₁₆,3w₁₆),(w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆), (−w₁₆,3w₁₆), (−w₁₆,w₁₆),(−w₁₆,−w₁₆), (−w₁₆,−3w₁₆), (−3w₁₆,3w₁₆), (−3w₁₆,w₁₆), (−3w₁₆,−w₁₆),(−3w₁₆,−3w₁₆)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, and b3. For example, in the case that the bits to be transmittedis (b0, b1, b2, b3)=(0, 0, 0, 0), the bits are mapped at signal point1001 in FIG. 10 , and (I,Q)=(3w₁₆,3w₁₆) is obtained when I is anin-phase component while Q is a quadrature component of the mappedbaseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3), in-phase componentI and quadrature component Q of the mapped baseband signal are decided(during 16QAM modulation). FIG. 10 illustrates an example of therelationship between the set of b0, b1, b2, and b3 (0000 to 1111) andthe signal point coordinates. Values 0000 to 1111 of the set of b0, b1,b2, and b3 are indicated immediately below 16 signal points included in16QAM (the marks “◯” in FIG. 10 ) (3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆),(3w₁₆,−3w₁₆), (w₁₆,3w₁₆), (w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆),(−w₁₆,3w₁₆), (−w₁₆,w₁₆), (−w₁₆,−w₁₆), (−w₁₆,−3w₁₆), (−3w₁₆,3w₁₆),(−3w₁₆,w₁₆), (−3w₁₆,−w₁₆), (−3w₁₆,−3w₁₆). Respective coordinates of thesignal points (“◯”) immediately above the values 0000 to 1111 of the setof b0, b1, b2, and b3 in the I-Q plane serve as in-phase component I andquadrature component Q of the mapped baseband signal. The relationshipbetween the set of b0, b1, b2, and b3 (0000 to 1111) and the signalpoint coordinates during 16QAM modulation is not limited to that in FIG.10 . A complex value of in-phase component I and quadrature component Qof the mapped baseband signal (during 16QAM modulation) serves as abaseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7 ).

The 64QAM mapping method will be described below. FIG. 11 illustrates anarrangement example of 64QAM signal points in the I-Q plane. In FIG. 11, 64 marks “◯” indicate 64QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 64 signal points included in 64QAM (indicated by themarks “◯” in FIG. 11 ) the I-Q are obtained as follows. (w₆₄ is a realnumber larger than 0)

(7w₆₄,7w₆₄), (7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄),(7w₆₄,−3w₆₄), (7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄) (−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄),(−w₆₄,w₆₄), (−w₆₄,−w₆₄), (−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, in the case that the bits to betransmitted is (b0, b1, b2, b3, b4, b5)=(0,0,0,0,0,0), the bits aremapped at signal point 1101 in FIG. 11 , and (I,Q)=(7w₆₄,7w₆₄) isobtained when I is an in-phase component while Q is a quadraturecomponent of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 11 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to of the set ofb0, b1, b2, b3, b4, and b5 are indicated immediately below 64 signalpoints included in 64QAM (the marks “◯” in FIG. 11 ) (7w₆₄,7w₆₄),(7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄), (7w₆₄,−3w₆₄),(7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄) (−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄),(−w₆₄,w₆₄), (−w₆₄,−w₆₄), (−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄,−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄). Respective coordinates ofthe signal points (“◯”) immediately above the values 000000 to 111111 ofthe set of b0, b1, b2, b3, b4, and b5 in the I-Q plane serve as in-phasecomponent I and quadrature component Q of the mapped baseband signal.The relationship between the set of b0, b1, b2, b3, b4, and b5 (000000to 111111) and the signal point coordinates during 64QAM modulation isnot limited to that in FIG. 11 . A complex value of in-phase component Iand quadrature component Q of the mapped baseband signal (during 64QAMmodulation) serves as a baseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7).

In this case, the modulation scheme of baseband signal 505A (s₁(t)(s₁(i))) is set to 16QAM while modulation scheme of baseband signal 505B(s₂(t) (s₂(i))) is set to 64QAM in FIG. 5 to FIG. 7 . The configurationof the precoding matrix will be described below.

At this point, generally average power of baseband signal 505A (s₁(t)and (s₁(i))) and average power of baseband signal 505B (s₂(t) and(s₂(i))), which are of the output of mapper 504 in FIGS. 5 to 7 , areequalized to each other. Accordingly, the following relationalexpression holds with respect to coefficient w₁₆ of the 16QAM mappingmethod and coefficient w₆₄ of the 64QAM mapping method.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 50} \right\rbrack & \; \\{w_{16} = \frac{z}{\sqrt{10}}} & \left( {S\mspace{14mu} 1\; 1} \right) \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 51} \right\rbrack & \; \\{w_{64} = \frac{z}{\sqrt{42}}} & \left( {S\mspace{14mu} 1\mspace{11mu} 2} \right)\end{matrix}$

In equations (S11) and (S12), it is assumed that z is a real numberlarger than 0. When the calculations are performed in <1> to <5>,

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

the configuration of precoding matrix F

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 52} \right\rbrack & \; \\{F = \begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}} & \left( {S\mspace{14mu} 1\mspace{11mu} 3} \right)\end{matrix}$

and a relationship between Q₁ and Q₂ will be described in detail below((Example 1-1) to (Example 1-8)).

Example 1-1

For one of <1> to <5>, precoding matrix F is set to one of the followingequations.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 53} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S14})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 54} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S15})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 55} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S16})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 56} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S17})}\end{matrix}$

In equations (S14), (S15), (S16), and (S17), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

In the configuration example (common to the description), “radian” isused as a phase unit such as an argument in a complex plane (the unit isindicated when “degree” is exceptionally used).

The use of the complex plane can display a polar coordinate of thecomplex number in terms of a polar form. Assuming that point (a, b) onthe complex plane is represented as [r,θ] in terms of the polarcoordinate when complex number z=a+jb (a and b are a real number and jis an imaginary unit) corresponds to point (a, b), the followingequation holds,a=r×cos θ, andb=r×sin θ  equation (49)In the equation, r is an absolute value of z (r=|z|) and θ is anargument, z=a+jb is represented as re^(jθ). For example, in e^(jπ) inequations (S14) to (S17), the unit of argument π is “radian”.

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 57} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}}} & {{Formula}\mspace{14mu}({S18})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 58} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}}} & {{Formula}\mspace{14mu}({S19})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 59} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4} \times e^{j\frac{\pi}{2}}}} & \left. {{Formula}\mspace{14mu}{S20}} \right) \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 60} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4} \times e^{j\frac{3\;\pi}{2}}}} & {{Formula}\mspace{14mu}({S21})}\end{matrix}$

The modulation scheme of baseband signal 505A (s₁(t) (s₁(i))) is set to16QAM while modulation scheme of baseband signal 505B (s₂(t) (s₂(i))) isset to 64QAM. Accordingly, the precoding (and the phase change and thepower change) is performed to transmit the modulated signal from eachantenna as described above, the total number of bits transmitted usingsymbols transmitted from antennas 808A and 808B in FIG. 8 at the (unit)time of time u and frequency (carrier) v is 10 bits that are of a sum of4 bits (for the use of 16QAM) and 6 bits (for the use of 64QAM).

Assuming that b_(0,16), b_(1,16), b_(2,16), and b_(3,16) are input bitsfor the purpose of the 16QAM mapping, and that b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64) and b_(5,64) are input bits for the purposeof the 64QAM mapping, even if value α in any one of equations (S18),(S19), (S20), and (S21) is used,

in signal z₁(t) (z₁(i)),

the signal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16),b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) correspondsto (0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16),b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64), b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) exist in theI-Q plane, similarly, in signal z₂(t) (z₂(i)),the signal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16),b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) correspondsto (0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16),b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64), b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) exist in theI-Q plane.

In the above description, with respect to signal z₁(t) (z₁(i)) inequations (s2), (S3), (S4), (S5), and (S8), equations (S18) to (S21) areconsidered as value α with which the receiver obtains the good datareception quality. This point will be described below.

In signal z₁(t) (z₁(i)),

the signal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16),b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) correspondsto (0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16),b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64), b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) exist in theI-Q plane, and it is desirable that 2¹⁰=1024 signal points exist in theI-Q plane while not overlapping one another.

This is attributed to the following fact. That is, the receiver performsthe detection and the error correction decoding using signal z₁(t)(z₁(i)) in the case that a modulated signal transmitted from the antennafor transmitting signal z₂(t) (z₂(i)) does not reach the receiver, andit is necessary at that time that the 1024 signal points exist in theI-Q plane while not overlapping one another in order that the receiverobtains the high data reception quality.

In the case that precoding matrix F is set to one of equations (S14),(S15), (S16), and (S17), and that α is set to one of equations (S18),(S19), (S20), and (S21), the arrangement of the signal point at which(b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64),b_(3,64), b_(4,64), b_(5,64)) corresponds to (0,0,0,0,0,0,0,0,0,0) tothe signal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16),b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) correspondsto (1,1,1,1,1,1,1,1,1,1) is obtained as illustrated in FIG. 12 in signalu₁(t) (u₁(i)) of configuration example R1 on the I-Q plane. In FIG. 12 ,a horizontal axis indicates I, and a vertical axis indicates Q, and amark “●” indicates a signal point.

As can be seen from FIG. 12 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S14),(S15), (S16), and (S17), and that α is set to one of equations (S18),(S19), (S20), and (S21), the arrangement of the signal point at which(b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64),b_(3,64), b_(4,64), b_(5,64)) corresponds to (0,0,0,0,0,0,0,0,0,0) tothe signal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16),b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) correspondsto (1,1,1,1,1,1,1,1,1,1) is obtained as illustrated in FIG. 13 in signalu₂(t) (u₂(i)) of configuration example R1 on the I-Q plane. In FIG. 13 ,a horizontal axis indicates I, and a vertical axis indicates Q, and amark “●” indicates a signal point.

As can be seen from FIG. 13 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 12 , and that D₂ is a minimum Euclidean distance at the1024 signal points in FIG. 13 . D₁> D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁>Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 1-2

Then, equations (S11) and (S12) hold with respect to coefficient w₁₆ ofthe 16QAM mapping method and coefficient w₆₄ of the 64QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 61} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S22})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 62} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S23})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 63} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S24})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 64} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S25})}\end{matrix}$

In equations (S22) and (S24), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 65} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}} \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S26})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 66} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S27})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 67} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}} \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S28})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 68} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S29})}\end{matrix}$

In equations (S26), (S27), (S28), and (S29), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 69} \right\rbrack & \; \\{{{- \frac{\pi}{2}}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}({radian})}} & {{Formula}\mspace{14mu}({S30})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S22),(S23), (S24), and (S25), and that θ is set to one of equations (S26),(S27), (S28), and (S29), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 12 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 12 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 12 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S22),(S23), (S24), and (S25), and that θ is set to one of equations (S26),(S27), (S28), and (S29), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 13 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 13 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 13 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 12 , and that D₂ is a minimum Euclidean distance at the1024 signal points in FIG. 13 . D₁>D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁>Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 1-3

Equations (S11) and (S12) hold with respect to coefficient w₁₆ of the16QAM mapping method and coefficient w₆₄ of the 64QAM mapping method,and precoding matrix F is set to one of equations (S22), (S23), (S24),and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 70} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S31})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 71} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S32})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 72} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S33})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 73} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S34})}\end{matrix}$

In equations (S31), (S32), (S33), and (S34), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 74} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}}} & {{Formula}\mspace{14mu}({S35})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 75} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}}} & {{Formula}\mspace{14mu}({S36})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 76} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5} \times e^{j\frac{\pi}{2}}}} & \left. {{Formula}\mspace{14mu}{S37}} \right) \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 77} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5} \times e^{j\frac{3\;\pi}{2}}}} & {{Formula}\mspace{14mu}({S38})}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S31),(S32), (S33), and (S34), and that α is set to one of equations (S35),(S36), (S37), and (S38), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 14 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 14 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 14 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S31),(S32), (S33), and (S34), and that α is set to one of equations (S35),(S36), (S37), and (S38), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 15 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 15 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 15 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 14 , and that D₂ is a minimum Euclidean distance at the1024 signal points in FIG. 15 . D₁>D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁>Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 1-4

Then, equations (S11) and (S12) hold with respect to coefficient w₁₆ ofthe 16QAM mapping method and coefficient w₆₄ of the 64QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 78} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S39})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 79} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S40})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 80} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S41})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 81} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S42})}\end{matrix}$

In equations (S39) and (S41), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 82} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}} \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S43})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 83} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S44})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 84} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}} \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S45})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 85} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S46})}\end{matrix}$

In equations (S43), (S44), (S45), and (S46), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 86} \right\rbrack & \; \\{{{- \frac{\pi}{2}}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}({radian})}} & {{Formula}\mspace{14mu}({S47})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S39),(S40), (S41), and (S42), and that θ is set to one of equations (S43),(S44), (S45), and (S46), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 14 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 14 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 14 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S39),(S40), (S41), and (S42), and that θ is set to one of equations (S43),(S44), (S45), and (S46), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 15 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 15 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 15 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 14 , and that D₂ is a minimum Euclidean distance at the1024 signal points in FIG. 15 . D₁>D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁>Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 1-5

Equations (S11) and (S12) hold with respect to coefficient w₁₆ of the16QAM mapping method and coefficient w₆₄ of the 64QAM mapping method,and precoding matrix F is set to one of equations (S22), (S23), (S24),and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 87} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S48})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 88} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S49})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 89} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S50})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 90} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S51})}\end{matrix}$

In equations (S48), (S49), (S50), and (S51), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 91} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}}} & {{Formula}\mspace{14mu}({S52})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 92} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}}} & {{Formula}\mspace{14mu}({S53})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 93} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4} \times e^{j\;\frac{\pi}{2}}}} & {{Formula}\mspace{14mu}({S54})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 94} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4} \times e^{j\;\frac{3\;\pi}{2}}}} & {{Formula}\mspace{14mu}({S55})}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S48),(S49), (S50), and (S51), and that α is set to one of equations (S52),(S53), (S54), and (S55), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 16 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 16 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 16 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S48),(S49), (S50), and (S51), and that α is set to one of equations (S52),(S53), (S54), and (S55), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 17 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 17 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 17 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 16 , and that D₁ is a minimum Euclidean distance at the1024 signal points in FIG. 17 . D₁<D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁<Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 1-6

Then, equations (S11) and (S12) hold with respect to coefficient w₁₆ ofthe 16QAM mapping method and coefficient w₆₄ of the 64QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 95} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S56})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 96} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S57})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 97} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S58})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 98} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S59})}\end{matrix}$

In equations (S56) and (S58), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 99} \right\rbrack & \; \\{\theta = {{\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}}} & {{Formula}\mspace{14mu}({S60})} \\{{\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}} \right)} + {2\; n\;\pi\mspace{14mu}({radian})}} & \; \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 100} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}({S61})} \\{\pi + {\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}} \right)} + {2\; n\;\pi\mspace{14mu}({radian})}} & \; \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 101} \right\rbrack & \; \\\begin{matrix}{\theta = {{\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}}} \\{{\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}} \right)} + {2\; n\;\pi\mspace{14mu}({radian})}}\end{matrix} & {{Formula}\mspace{14mu}({S62})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 102} \right\rbrack & \; \\\begin{matrix}{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}}}} \\{\pi + {\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}} \right)} + {2\; n\;\pi\mspace{14mu}({radian})}}\end{matrix} & {{Formula}\mspace{14mu}({S63})}\end{matrix}$

In equations (S60), (S61), (S62), and (S63), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 103} \right\rbrack & \; \\{{{- \frac{\pi}{2}}\mspace{14mu}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}\mspace{14mu}({radian})}} & {{Formula}\mspace{14mu}({S64})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S56),(S57), (S58), and (S59), and that θ is set to one of equations (S60),(S61), (S62), and (S63), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 16 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 16 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 16 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S56),(S57), (S58), and (S59), and that θ is set to one of equations (S60),(S61), (S62), and (S63), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 17 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 17 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 17 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 16 , and that D₁ is a minimum Euclidean distance at the1024 signal points in FIG. 17 . D₁<D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁<Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 1-7

Equations (S11) and (S12) hold with respect to coefficient w₁₆ of the16QAM mapping method and coefficient w₆₄ of the 64QAM mapping method,and precoding matrix F is set to one of equations (S22), (S23), (S24),and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 104} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 65} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 105} \right\rbrack & \; \\{{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 66} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 106} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 67} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 107} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}\left( {S\; 68} \right)}\end{matrix}$

In equations (S65), (S66), (S67), and (S68), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 108} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 69} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 109} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}}} & {{Formula}\mspace{14mu}\left( {S\; 70} \right)}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 110} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5} \times e^{j\frac{\pi}{2}}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 71} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 111} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}\left( {S\; 72} \right)}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S65),(S66), (S67), and (S68), and that α is set to one of equations (S69),(S70), (S71), and (S72), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 18 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 18 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 18 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S65),(S66), (S67), and (S68), and that α is set to one of equations (S69),(S70), (S71), and (S72), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 19 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 19 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 19 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 18 , and that D₁ is a minimum Euclidean distance at the1024 signal points in FIG. 19 . D₁<D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁<Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 1-8

Then, equations (S11) and (S12) hold with respect to coefficient w₁₆ ofthe 16QAM mapping method and coefficient w₆₄ of the 64QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 112} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{14mu}\theta} & {\beta \times \sin\mspace{14mu}\theta} \\{\beta \times \sin\mspace{14mu}\theta} & {{- \beta} \times \cos\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 73} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 113} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\mspace{14mu}\theta} & {\sin\mspace{14mu}\theta} \\{\sin\mspace{14mu}\theta} & {{- \cos}\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 74} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 114} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{14mu}\theta} & {{- \beta} \times \sin\mspace{14mu}\theta} \\{\beta \times \sin\mspace{14mu}\theta} & {\beta \times \cos\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 75} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 115} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\mspace{14mu}\theta} & {{- \sin}\mspace{14mu}\theta} \\{\sin\mspace{14mu}\theta} & {\cos\mspace{14mu}\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}\left( {S\; 76} \right)}\end{matrix}$

In equations (S73) and (S75), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 116} \right\rbrack} & \; \\{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}} \right)}} + {2n\;\pi\mspace{14mu}({radian})\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}\left( {S\; 77} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 117} \right\rbrack} & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}} \right)} + {2n\;\pi\mspace{14mu}({radian})\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}\left( {S\; 78} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 118} \right\rbrack} & \; \\{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{4}{5}} \right)}} + {2n\;\pi\mspace{14mu}({radian})\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}\left( {S\; 79} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 119} \right\rbrack} & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{4}{5}} \right)} + {2n\;\pi\mspace{14mu}({radian})}}} & {{Formula}\mspace{14mu}\left( {S\; 80} \right)}\end{matrix}$

In equations (S77), (S78), (S79), and (S80), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 120} \right\rbrack & \; \\{{{- \frac{\pi}{2}}\mspace{14mu}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}\mspace{14mu}({radian})}} & {{Formula}\mspace{14mu}\left( {S\; 81} \right)}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S73),(S74), (S75), and (S76), and that θ is set to one of equations (S77),(S78), (S79), and (S80), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 18 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 18 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 18 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S73),(S74), (S75), and (S76), and that θ is set to one of equations (S77),(S78), (S79), and (S80), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 19 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 19 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 19 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 18 , and that D₁ is a minimum Euclidean distance at the1024 signal points in FIG. 19 . D₁<D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁<Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 1-Supplement

Values α and θ having the possibility of achieving the high datareception quality are illustrated in (Example 1-1) to (Example 1-8).However, even if values α and θ are not those in (Example 1-1) to(Example 1-8), sometimes the high data reception quality is obtained bysatisfying the condition of configuration example R1.

Example 2

In mapper 504 of FIGS. 5 to 7 , the modulation scheme for obtainings₁(t) (s₁(i)) is set to 64QAM while the modulation scheme for obtainings₂(t) (s₂(i)) is set to 16QAM. An example of conditions associated withthe configuration and power change of precoding matrix (F) when theprecoding and/or the power change is performed on, for example, one ofequations (s2), (S3), (S4), (S5), and (S8) will be described below.

The 16QAM mapping method will be described below. FIG. 10 illustrates anarrangement example of 16QAM signal points in the I-Q plane. In FIG. 10, 16 marks “◯” indicate 16QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 16 signal points included in 16QAM (indicated by themarks “◯” in FIG. 10 ) in the I-Q are obtained as follows. (w₁₆ is areal number larger than 0) (3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆),(3w₁₆,−3w₁₆), (w₁₆,3w₁₆), (w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆),(−w₁₆,3w₁₆), (−w₁₆,w₁₆), (−w₁₆,−w₁₆), (−w₁₆, −3w₁₆), (−3w₁₆,3w₁₆),(−3w₁₆,w₁₆), (−3w₁₆,−w₁₆), (−3w₁₆,−3w₁₆)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, and b3. For example, in the case that the bits to be transmittedis (b0, b1, b2, b3)=(0,0,0,0), the bits are mapped at signal point 1001in FIG. 10 , and (I,Q)=(3w₁₆,3w₁₆) is obtained when I is an in-phasecomponent while Q is a quadrature component of the mapped basebandsignal.

Based on the bits to be transmitted (b0, b1, b2, b3), in-phase componentI and quadrature component Q of the mapped baseband signal are decided(during 16QAM modulation). FIG. 10 illustrates an example of therelationship between the set of b0, b1, b2, and b3 (0000 to 1111) andthe signal point coordinates. Values 0000 to 1111 of the set of b0, b1,b2, and b3 are indicated immediately below 16 signal points included in16QAM (the marks “◯” in FIG. 10 ) (3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆),(3w₁₆,−3w₁₆), (w₁₆,3w₁₆), (w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆),(−w₁₆,3w₁₆), (−w₁₆,w₁₆), (−w₁₆,−w₁₆), (−w₁₆,−3w₁₆), (−3w₁₆,3w₁₆),(−3w₁₆,w₁₆), (−3w₁₆,−w₁₆), (−3w₁₆,−3w₁₆). Respective coordinates of thesignal points (“◯”) immediately above the values 0000 to 1111 of the setof b0, b1, b2, and b3 in the I-Q plane serve as in-phase component I andquadrature component Q of the mapped baseband signal. The relationshipbetween the set of b0, b1, b2, and b3 (0000 to 1111) and the signalpoint coordinates during 16QAM modulation is not limited to that in FIG.10 . A complex value of in-phase component I and quadrature component Qof the mapped baseband signal (during 16QAM modulation) serves as abaseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7 ).

The 64QAM mapping method will be described below. FIG. 11 illustrates anarrangement example of 64QAM signal points in the I-Q plane. In FIG. 11, 64 marks “◯” indicate 64QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 64 signal points include in 64QAM (indicated by themarks “◯” in FIG. 11 ) in the I-Q are obtained as follows. (w₆₄ is areal number larger than 0)

(7w₆₄,7w₆₄), (7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄),(7w₆₄,−3w₆₄), (7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄) (−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄),(−w₆₄,w₆₄), (−w₆₄,−w₆₄), (−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, in the case that the bits to betransmitted is (b0, b1, b2, b3, b4, b5)=(0,0,0,0,0,0), the bits aremapped at signal point 1101 in FIG. 11 , and (I,Q)=(7w₆₄,7w₆₄) isobtained when I is an in-phase component while Q is a quadraturecomponent of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 11 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to of the set ofb0, b1, b2, b3, b4, and b5 are indicated immediately below 64 signalpoints included in 64QAM (the marks “◯” in FIG. 11 ) (7w₆₄,7w₆₄),(7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄), (7w₆₄,−3w₆₄),(7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄) (−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄),(−w₆₄,w₆₄), (−w₆₄,−w₆₄), (−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄₇w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄). Respective coordinates ofthe signal points (“◯”) immediately above the values 000000 to 111111 ofthe set of b0, b1, b2, b3, b4, and b5 in the I-Q plane serve as in-phasecomponent I and quadrature component Q of the mapped baseband signal.The relationship between the set of b0, b1, b2, b3, b4, and b5 (000000to 111111) and the signal point coordinates during 64QAM modulation isnot limited to that in FIG. 11 . A complex value of in-phase component Iand quadrature component Q of the mapped baseband signal (during 64QAMmodulation) serves as a baseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7).

In this case, the modulation scheme of baseband signal 505A (s₁(t)(s₁(i))) is set to 64QAM while modulation scheme of baseband signal 505B(s₂(t) (s₂(i))) is set to 16QAM in FIG. 5 to FIG. 7 . The configurationof the precoding matrix will be described below.

At this point, generally average power of baseband signal 505A (s₁(t)and (s₁(i))) and average power of baseband signal 505B (s₂(t) and(s₂(i))), which are of the output of mapper 504 in FIGS. 5 to 7 , areequalized to each other. Accordingly, the following relationalexpression holds with respect to coefficient w₁₆ of the 16QAM mappingmethod and coefficient w₆₄ of the 64QAM mapping method.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 121} \right\rbrack & \; \\{w_{16} = \frac{z}{\sqrt{10}}} & ({S82}) \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 122} \right\rbrack & \; \\{w_{64} = \frac{z}{\sqrt{42}}} & ({S83})\end{matrix}$

In equations (S82) and (S83), it is assumed that z is a real numberlarger than 0. When the calculations are performed in <1> to <5>,

<1> For P₁ ²=P₂ ² in equation (S2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

the configuration of precoding matrix F

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 123} \right\rbrack & \; \\{F = \begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}} & ({S84})\end{matrix}$

and a relationship between Q₁ and Q₂ will be described in detail below((Example 2-1) to (Example 2-8)).

Example 2-1

For one of <1> to <5>, precoding matrix F is set to one of the followingequations.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 124} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S85})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 125} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S86})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 126} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S87})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 127} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S88})}\end{matrix}$

In equations (S85), (S86), (S87), and (S88), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 128} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}}} & {{Formula}\mspace{14mu}({S89})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 129} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}}} & {{Formula}\mspace{14mu}({S90})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 130} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4} \times e^{j\frac{\pi}{2}}}} & {{Formula}\mspace{14mu}({S91})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 131} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}({S92})}\end{matrix}$

The modulation scheme of baseband signal 505A (s₁(t) (s₁(i))) is set to64QAM while modulation scheme of baseband signal 505B (s₂(t) (s₂(i))) isset to 16QAM. Accordingly, the precoding (and the phase change and thepower change) is performed to transmit the modulated signal from eachantenna as described above, the total number of bits transmitted usingsymbols transmitted from antenna 808A and 808B in FIG. 8 at the (unit)time of time u and frequency (carrier) v is 10 bits that are of a sum of4 bits (for the use of 16QAM) and 6 bits (for the use of 64QAM).

Assuming that b_(0.16), b_(1,16), b_(2,16), and b_(3,16) are input bitsfor the purpose of the 16QAM mapping, and that b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64) and b_(5,64) are input bits for the purposeof the 64QAM mapping, even if value α in any one of equations (S89),(S90), (S91), and (S92) is used,

in signal z₁(t) (z₁(i)),

the signal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16),b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) correspondsto (0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16),b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64), b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) exist in theI-Q plane, similarly, in signal z₂(t) (z₂(i)),the signal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16),b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) correspondsto (0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16),b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64), b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) exist in theI-Q plane.

In the above description, with respect to signal z₂(t) (z₂(i)) inequations (s2), (S3), (S4), (S5), and (S8), equations (S89) to (S92) areconsidered as value α with which the receiver obtains the good datareception quality. This point will be described below. In signal z₂(t)(z₂(i)), the signal point at which (b_(0,16), b_(1,16), b_(2,16),b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64))corresponds to (0,0,0,0,0,0,0,0,0,0) to the signal point at which(b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64),b_(3,64), b_(4,64), b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) existin the I-Q plane, and it is desirable that 2¹⁰=1024 signal points existin the I-Q plane while not overlapping one another.

This is attributed to the following fact. That is, the receiver performsthe detection and the error correction decoding using signal z₂(t)(z₂(i)) in the case that a modulated signal transmitted from the antennafor transmitting signal z₁(t) (z₁(i)) does not reach the receiver, andit is necessary at that time that the 1024 signal points exist in theI-Q plane while not overlapping one another in order that the receiverobtains the high data reception quality.

In the case that precoding matrix F is set to one of equations (S85),(S86), (S87), and (S88), and that α is set to one of equations (S89),(S90), (S91), and (S92), the arrangement of the signal point at which(b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64),b_(3,64), b_(4,64), b_(5,64)) corresponds to (0,0,0,0,0,0,0,0,0,0) tothe signal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16),b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) correspondsto (1,1,1,1,1,1,1,1,1,1) is obtained as illustrated in FIG. 16 in signalu₂(t) (u₂(i)) of configuration example R1 on the I-Q plane. In FIG. 16 ,a horizontal axis indicates I, and a vertical axis indicates Q, and amark “●” indicates a signal point.

As can be seen from FIG. 16 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S85),(S86), (S87), and (S88), and that α is set to one of equations (S89),(S90), (S91), and (S92), the arrangement of the signal point at which(b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64),b_(3,64), b_(4,64), b_(5,64)) corresponds to (0,0,0,0,0,0,0,0,0,0) tothe signal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16),b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) correspondsto (1,1,1,1,1,1,1,1,1,1) is obtained as illustrated in FIG. 17 in signalu₁(t) (u₁(i)) of configuration example R1 on the I-Q plane. In FIG. 17 ,a horizontal axis indicates I, and a vertical axis indicates Q, and amark “●” indicates a signal point.

As can be seen from FIG. 17 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 16 , and that D₁ is a minimum Euclidean distance at the1024 signal points in FIG. 17 . D₁<D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁<Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 2-2

Then, equations (S11) and (S12) hold with respect to coefficient w₁₆ ofthe 16QAM mapping method and coefficient w₆₄ of the 64QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 132} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S93})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 133} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S94})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 134} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S95})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 135} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S96})}\end{matrix}$

In equations (S93) and (S95), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 136} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}} \right)}} + {2\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S97})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 137} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{5}{4}} \right)} + {2\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S98})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 138} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}} \right)}} + {2\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S99})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 139} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{5}{4}} \right)} + {2\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S100})}\end{matrix}$

In equations (S97), (S98), (S99), and (S100), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 140} \right\rbrack & \; \\{{{- \frac{\pi}{2}}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}({radian})}} & {{Formula}\mspace{14mu}({S101})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S93),(S94), (S95), and (S96), and that θ is set to one of equations (S97),(S98), (S99), and (S100), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64) b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 16 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 16 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 16 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S93),(S94), (S95), and (S96), and that θ is set to one of equations (S97),(S98), (S99), and (S100), similarly the arrangement of the signal pointat which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64), b_(1,64),b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 17 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 17 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 17 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 16 , and that D₁ is a minimum Euclidean distance at the1024 signal points in FIG. 17 . D₁<D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁<Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 2-3

Equations (S11) and (S12) hold with respect to coefficient w₁₆ of the16QAM mapping method and coefficient w₆₄ of the 64QAM mapping method,and precoding matrix F is set to one of equations (S22), (S23), (S24),and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 141} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j0}} & {\beta \times \alpha \times e^{j0}} \\{\beta \times \alpha \times e^{j0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S102})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 142} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j0} & {\alpha \times e^{j0}} \\{\alpha \times e^{j0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S103})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 143} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S104})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 144} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S105})}\end{matrix}$

In equations (S102), (S103), (S104), and (S105), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 145} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}}} & {{Formula}\mspace{14mu}({S106})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 146} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}}} & {{Formula}\mspace{14mu}({S107})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 147} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5} \times e^{j\frac{\pi}{2}}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 108} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 148} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}\left( {S\; 109} \right)}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S102),(S103), (S104), and (S105), and that α is set to one of equations(S106), (S107), (S108), and (S109), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 18 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 18 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 18 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S102),(S103), (S104), and (S105), and that α is set to one of equations(S106), (S107), (S108), and (S109), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 19 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 19 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 19 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 18 , and that D₁ is a minimum Euclidean distance at the1024 signal points in FIG. 19 . D₁<D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁<Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 2-4

Then, equations (S11) and (S12) hold with respect to coefficient w₁₆ ofthe 16QAM mapping method and coefficient w₆₄ of the 64QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 149} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S110})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 150} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S111})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 151} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S112})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 152} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S113})}\end{matrix}$

In equations (S110) and (S112), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 153} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}} \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S114})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 154} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{10}} \times \frac{4}{5}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S115})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 155} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}} \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S116})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 156} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{10}}} \times \frac{4}{5}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S117})}\end{matrix}$

In equations (S114), (S115), (S116), and (S117), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 157} \right\rbrack & \; \\{{{- \frac{\pi}{2}}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}({radian})}} & {{Formula}\mspace{14mu}({S118})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S110),(S111), (S112), and (S113), and that θ is set to one of equations(S114), (S115), (S116), and (S117), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 18 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 18 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 18 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S110),(S111), (S112), and (S113), and that θ is set to one of equations(S114), (S115), (S116), and (S117), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 19 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 19 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 19 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 18 , and that D₁ is a minimum Euclidean distance at the1024 signal points in FIG. 19 . D₁<D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁<Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 2-5

Equations (S11) and (S12) hold with respect to coefficient w₁₆ of the16QAM mapping method and coefficient w₆₄ of the 64QAM mapping method,and precoding matrix F is set to one of equations (S22), (S23), (S24),and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 158} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S119})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 159} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{a^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S120})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 160} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S121})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 161} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{a^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S122})}\end{matrix}$

In equations (S119), (S120), (S121), (S122), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 162} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}}} & {{Formula}\mspace{14mu}({S123})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 163} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}}} & {{Formula}\mspace{14mu}({S124})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 164} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4} \times e^{j\frac{\pi}{2}}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 125} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 165} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}\left( {S\; 126} \right)}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S119),(S120), (S121), and (S122), and that α is set to one of equations(S123), (S124), (S125), and (S126), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 12 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 12 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 12 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S119),(S120), (S121), and (S122), and that α is set to one of equations(S123), (S124), (S125), and (S126), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 13 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 13 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 13 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 12 , and that D₂ is a minimum Euclidean distance at the1024 signal points in FIG. 13 . D₁>D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁>Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 2-6

Then, equations (S11) and (S12) hold with respect to coefficient w₁₆ ofthe 16QAM mapping method and coefficient w₆₄ of the 64QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 166} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S127})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 167} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S128})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 168} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S129})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 169} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S130})}\end{matrix}$

In equations (S127) and (S129), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 170} \right\rbrack & \; \\{\theta = {{\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}} \right)\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}} \right)}} + {2{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S131})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 171} \right\rbrack & \; \\{\theta = {\pi + {\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}} \right)\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{5}{4}} \right)} + {2{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S132})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 172} \right\rbrack & \; \\{\theta = {{\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}} \right)\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}} \right)}} + {2{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S133})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 173} \right\rbrack & \; \\{\theta = {\pi + {\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}} \right)\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{5}{4}} \right)} + {2{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S134})}\end{matrix}$

In equations (S131), (S132), (S133), and (S134), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 174} \right\rbrack & \; \\{{{- \frac{\pi}{2}}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}({radian})}} & {{Formula}\mspace{14mu}({S135})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S127),(S128), (S129), and (S130), and that θ is set to one of equations(S131), (S132), (S133), and (S134), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 12 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 12 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 12 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S127),(S128), (S129), and (S130), and that θ is set to one of equations(S131), (S132), (S133), and (S134), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 13 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 13 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 13 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 12 , and that D₂ is a minimum Euclidean distance at the1024 signal points in FIG. 13 . D₁>D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁>Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 2-7

Equations (S11) and (S12) hold with respect to coefficient w₁₆ of the16QAM mapping method and coefficient w₆₄ of the 64QAM mapping method,and precoding matrix F is set to one of equations (S22), (S23), (S24),and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 175} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j0}} & {\beta \times \alpha \times e^{j0}} \\{\beta \times \alpha \times e^{j0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S136})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 176} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j0} & {\alpha \times e^{j0}} \\{\alpha \times e^{j0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S137})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 177} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S138})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 178} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S139})}\end{matrix}$

In equations (S136), (S137), (S138), and (S139), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 179} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 140} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 180} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{4}{5}}} & {{Formula}\mspace{14mu}\left( {S\; 141} \right)}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 181} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5} \times e^{j\frac{\pi}{2}}}} & {{Formula}\mspace{14mu}({S142})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 182} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}({S143})}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S136),(S137), (S138), and (S139), and that α is set to one of equations(S140), (S141), (S142), and (S143), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 14 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 14 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 14 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S136),(S137), (S138), and (S139), and that α is set to one of equations(S140), (S141), (S142), and (S143), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 15 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 15 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 15 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 14 , and that D₂ is a minimum Euclidean distance at the1024 signal points in FIG. 15 . D₁>D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁>Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 2-8

Then, equations (S11) and (S12) hold with respect to coefficient w₁₆ ofthe 16QAM mapping method and coefficient w₆₄ of the 64QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 183} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S144})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 184} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S145})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 185} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S146})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 186} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S147})}\end{matrix}$

In equations (S144) and (S146), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 187} \right\rbrack & \; \\{{{\theta = {\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}} \right)}}{or}{\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}} \right)} + {2n\;{\pi({radian})}}}{or}} & {{Formula}\mspace{14mu}({S148})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 188} \right\rbrack & \; \\{{{\theta = {\pi + {\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}} \right)}}}{or}\pi + {\tan^{- 1}\left( {\frac{\sqrt{10}}{\sqrt{42}} \times \frac{4}{5}} \right)} + {2n\;{\pi({radian})}}}{or}} & {{Formula}\mspace{14mu}({S149})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 189} \right\rbrack & \; \\{{{\theta = {\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{4}{5}} \right)}}{or}{\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{4}{5}} \right)} + {2n\;{\pi({radian})}}}{or}} & {{Formula}\mspace{14mu}({S150})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 190} \right\rbrack & \; \\{{\theta = {\pi + {\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{4}{5}} \right)}}}{or}{\pi + {\tan^{- 1}\left( {{- \frac{\sqrt{10}}{\sqrt{42}}} \times \frac{4}{5}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S151})}\end{matrix}$

In equations (S148), (S149), (S150), and (S151), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 191} \right\rbrack & \; \\{{{- \frac{\pi}{2}}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}({radian})}} & {{Formula}\mspace{14mu}({S152})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S144),(S145), (S146), and (S147), and that θ is set to one of equations(S148), (S149), (S150), and (S151), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 14 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 14 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 14 , the 1024 signal points exist while notoverlapping one another. On the I-Q plane, Euclidean distances betweenclosest signal points are equal in the 1020 signal points of the 1024signal points except for a rightmost and uppermost point, a rightmostand lowermost point, a leftmost and uppermost point, and a leftmost andlowermost point. Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S144),(S145), (S146), and (S147), and that θ is set to one of equations(S148), (S149), (S150), and (S151), similarly the arrangement of thesignal point at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 15 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 15 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 15 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 14 , and that D₂ is a minimum Euclidean distance at the1024 signal points in FIG. 15 . D₁>D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁>Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 2—Supplement

Values α and θ having the possibility of achieving the high datareception quality are illustrated in (Example 2-1) to (Example 2-8).However, even if values α and θ are not those in (Example 2-1) to(Example 2-8), sometimes the high data reception quality is obtained bysatisfying the condition of configuration example R1.

Example 3

In mapper 504 of FIGS. 5 to 7 , the modulation scheme for obtainings₁(t) (s₁(i)) is set to 64QAM while the modulation scheme for obtainings₂(t) (s₂(i)) is set to 256QAM. An example of conditions associated withthe configuration and power change of precoding matrix (F) when theprecoding and/or the power change is performed on, for example, one ofequations (s2), (S3), (S4), (S5), and (S8) will be described below.

The 64QAM mapping method will be described below. FIG. 11 illustrates anarrangement example of 64QAM signal points in the I-Q plane. In FIG. 11, 64 marks “◯” indicate 64QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 64 signal points included in 64QAM (indicated by themarks “◯” in FIG. 11 ) are obtained as follows. (w₆₄ is a real numberlarger than 0)

(7w₆₄,7w₆₄), (7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄),(7w₆₄,−3w₆₄), (7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄) (−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄),(−w₆₄,w₆₄), (−w₆₄,−w₆₄), (−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, in the case that the bits to betransmitted is (b0, b1, b2, b3, b4, b5)=(0,0,0,0,0,0), the bits aremapped at signal point 1101 in FIG. 11 , and (I,Q)=(7w₆₄,7w₆₄) isobtained when I is an in-phase component while Q is a quadraturecomponent of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 11 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to of the set ofb0, b1, b2, b3, b4, and b5 are indicated immediately below 64 signalpoints included in 64QAM (the marks “◯” in FIG. 11 ) (7w₆₄,7w₆₄),(7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄), (7w₆₄,−3w₆₄),(7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄)

(−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄), (−w₆₄,w₆₄), (−w₆₄,−w₆₄),(−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄, −7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄). Respective coordinates ofthe signal points (“◯”) immediately above the values 000000 to 111111 ofthe set of b0, b1, b2, b3, b4, and b5 in the I-Q plane serve as in-phasecomponent I and quadrature component Q of the mapped baseband signal.The relationship between the set of b0, b1, b2, b3, b4, and b5 (000000to 111111) and the signal point coordinates during 64QAM modulation isnot limited to that in FIG. 11 . A complex value of in-phase component Iand quadrature component Q of the mapped baseband signal (during 64QAMmodulation) serves as a baseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7).

The 256QAM mapping method will be described below. FIG. 20 illustratesan arrangement example of 256QAM signal points in the I-Q plane. In FIG.20 , 256 marks “◯” indicate the 256QAM signal points.

In the I-Q plane, 256 signal points included in 256QAM (indicated by themarks “◯” in FIG. 20 ) are obtained as follows. (w₂₅₆ is a real numberlarger than 0)

(15w₂₅₆,15w₂₅₆), (15w₂₅₆,13w₂₅₆), (15w₂₅₆,11w₂₅₆), (15w₂₅₆,9w₂₅₆),(15w₂₅₆,7w₂₅₆), (15w₂₅₆,5w₂₅₆), (15w₂₅₆,3w₂₅₆), (15w₂₅₆,w₂₅₆),

(15w₂₅₆,−15w₂₅₆), (15w₂₅₆,−13w₂₅₆), (15w₂₅₆,−11w₂₅₆), (15w₂₅₆,−9w₂₅₆),(15w₂₅₆,−7w₂₅₆), (15w₂₅₆,−5w₂₅₆), (15w₂₅₆,−3w₂₅₆), (15w₂₅₆,−w₂₅₆),

(13w₂₅₆,15w₂₅₆), (13w₂₅₆,13w₂₅₆), (13w₂₅₆,11w₂₅₆), (13w₂₅₆,9w₂₅₆),(13w₂₅₆,7w₂₅₆), (13w₂₅₆,5w₂₅₆), (13w₂₅₆,3w₂₅₆), (13w₂₅₆,w₂₅₆),

(13w₂₅₆,−15w₂₅₆), (13w₂₅₆,−13w₂₅₆), (13w₂₅₆,−11w₂₅₆), (13w₂₅₆,−9w₂₅₆),(13w₂₅₆,−7w₂₅₆), (13w₂₅₆,−5w₂₅₆), (13w₂₅₆,−3w₂₅₆), (13w₂₅₆,−w₂₅₆),

(11w₂₅₆,15w₂₅₆), (11w₂₅₆,13w₂₅₆), (11w₂₅₆,11w₂₅₆), (11w₂₅₆,9w₂₅₆),(11w₂₅₆,7w₂₅₆), (11w₂₅₆,5w₂₅₆), (11w₂₅₆,3w₂₅₆), (11w₂₅₆,w₂₅₆),

(11w₂₅₆,−15w₂₅₆), (11w₂₅₆,−13w₂₅₆), (11w₂₅₆,−11w₂₅₆), (11w₂₅₆,−9w₂₅₆),(11w₂₅₆,−7w₂₅₆), (11w₂₅₆,−5w₂₅₆), (11w₂₅₆,−3w₂₅₆), (11w₂₅₆,−w₂₅₆),

(9w₂₅₆,15w₂₅₆), (9w₂₅₆,13w₂₅₆), (9w₂₅₆,11w₂₅₆), (9w₂₅₆,9w₂₅₆),(9w₂₅₆,7w₂₅₆), (9w₂₅₆,5w₂₅₆), (9w₂₅₆,3w₂₅₆), (9w₂₅₆,w₂₅₆),

(9w₂₅₆,−15w₂₅₆), (9w₂₅₆,−13w₂₅₆), (9w₂₅₆,−11w₂₅₆), (9w₂₅₆,−9w₂₅₆),(9w₂₅₆,−7w₂₅₆), (9w₂₅₆,−5w₂₅₆), (9w₂₅₆,−3w₂₅₆), (9w₂₅₆,−w₂₅₆),

(7w₂₅₆,15w₂₅₆), (7w₂₅₆,13w₂₅₆), (7w₂₅₆,11w₂₅₆), (7w₂₅₆,9w₂₅₆),(7w₂₅₆,7w₂₅₆), (7w₂₅₆,5w₂₅₆), (7w₂₅₆,3w₂₅₆), (7w₂₅₆,w₂₅₆),

(7w₂₅₆,−15w₂₅₆), (7w₂₅₆,−13w₂₅₆), (7w₂₅₆,−11w₂₅₆), (7w₂₅₆,−9w₂₅₆),(7w₂₅₆,−7w₂₅₆), (7w₂₅₆,−5w₂₅₆), (7w₂₅₆,−3w₂₅₆), (7w₂₅₆,−w₂₅₆),

(5w₂₅₆,15w₂₅₆), (5w₂₅₆,13w₂₅₆), (5w₂₅₆,11w₂₅₆), (5w₂₅₆,9w₂₅₆),(5w₂₅₆,7w₂₅₆), (5w₂₅₆,5w₂₅₆), (5w₂₅₆,3w₂₅₆), (5w₂₅₆,w₂₅₆),

(5w₂₅₆,−15w₂₅₆), (5w₂₅₆,−13w₂₅₆), (5w₂₅₆,−11w₂₅₆), (5w₂₅₆,−9w₂₅₆),(5w₂₅₆,−7w₂₅₆), (5w₂₅₆,−5w₂₅₆), (5w₂₅₆,−3w₂₅₆), (5w₂₅₆,−w₂₅₆),

(3w₂₅₆,15w₂₅₆), (3w₂₅₆,13w₂₅₆), (3w₂₅₆,11w₂₅₆), (3w₂₅₆,9w₂₅₆),(3w₂₅₆,7w₂₅₆), (3w₂₅₆,5w₂₅₆), (3w₂₅₆,3w₂₅₆), (3w₂₅₆,w₂₅₆),

(3w₂₅₆,−15w₂₅₆), (3w₂₅₆,−13w₂₅₆), (3w₂₅₆,−11w₂₅₆), (3w₂₅₆,−9w₂₅₆),(3w₂₅₆,−7w₂₅₆), (3w₂₅₆,−5w₂₅₆), (3w₂₅₆,−3w₂₅₆), (3w₂₅₆,−w₂₅₆),

(w₂₅₆,15w₂₅₆), (w₂₅₆,13w₂₅₆), (w₂₅₆,11w₂₅₆), (w₂₅₆,9w₂₅₆), (w₂₅₆,7w₂₅₆),(w₂₅₆,5w₂₅₆), (w₂₅₆,3w₂₅₆), (w₂₅₆,w₂₅₆),

(w₂₅₆,−15w₂₅₆), (w₂₅₆,−13w₂₅₆), (w₂₅₆,−11w₂₅₆), (w₂₅₆,−9w₂₅₆),(w₂₅₆,−7w₂₅₆), (w₂₅₆,−5w₂₅₆), (w₂₅₆,−3w₂₅₆), (w₂₅₆,−w₂₅₆),

(−15w₂₅₆,15w₂₅₆), (−15w₂₅₆,13w₂₅₆), (−15w₂₅₆,11w₂₅₆), (−15w₂₅₆,9w₂₅₆),(−15w₂₅₆,7w₂₅₆), (−15w₂₅₆,5w₂₅₆), (−15w₂₅₆,3w₂₅₆), (−15w₂₅₆,w₂₅₆),

(−15w₂₅₆,−15w₂₅₆), (−15w₂₅₆,−13w₂₅₆), (−15w₂₅₆,−11w₂₅₆),(−15w₂₅₆,−9w₂₅₆), (−15w₂₅₆,−7w₂₅₆), (−15w₂₅₆,−5w₂₅₆), (−15w₂₅₆,−3w₂₅₆),(−15w₂₅₆,−w₂₅₆),

(−13w₂₅₆,15w₂₅₆), (−13w₂₅₆,13w₂₅₆), (−13w₂₅₆,11w₂₅₆), (−13w₂₅₆,9w₂₅₆),(−13w₂₅₆,7w₂₅₆),

(−13w₂₅₆,5w₂₅₆), (−13w₂₅₆,3w₂₅₆), (−13w₂₅₆,w₂₅₆), (−13w₂₅₆,−15w₂₅₆),(−13w₂₅₆,−13w₂₅₆), (−13w₂₅₆,−11w₂₅₆), (−13w₂₅₆,−9w₂₅₆),(−13w₂₅₆,−7w₂₅₆), (−13w₂₅₆,−5w₂₅₆), (−13w₂₅₆,−3w₂₅₆), (−13w₂₅₆,−w₂₅₆),

(−11w₂₅₆,15w₂₅₆), (−11w₂₅₆,13w₂₅₆), (−11w₂₅₆,11w₂₅₆), (−11w₂₅₆,9w₂₅₆),(−11w₂₅₆,7w₂₅₆), (−11w₂₅₆,5w₂₅₆), (−11w₂₅₆,3w₂₅₆), (−11w₂₅₆,w₂₅₆),

(−11w₂₅₆,−15w₂₅₆), (−11w₂₅₆,−13w₂₅₆), (−11w₂₅₆,−11w₂₅₆),(−11w₂₅₆,−9w₂₅₆), (−11w₂₅₆,−7w₂₅₆), (−11w₂₅₆,−5w₂₅₆), (−11w₂₅₆,−3w₂₅₆),(−11w₂₅₆,−w₂₅₆),

(−9w₂₅₆,15w₂₅₆), (−9w₂₅₆,13w₂₅₆), (−9w₂₅₆,11w₂₅₆), (−9w₂₅₆,9w₂₅₆),(−9w₂₅₆,7w₂₅₆), (−9w₂₅₆,5w₂₅₆), (−9w₂₅₆,3w₂₅₆), (−9w₂₅₆,w₂₅₆),

(−9w₂₅₆,−15w₂₅₆), (−9w₂₅₆,−13w₂₅₆), (−9w₂₅₆,−11w₂₅₆), (−9w₂₅₆,−9w₂₅₆),(−9w₂₅₆,−7w₂₅₆), (−9w₂₅₆,−5w₂₅₆), (−9w₂₅₆,−3w₂₅₆), (−9w₂₅₆,−w₂₅₆),

(−7w₂₅₆,15w₂₅₆), (−7w₂₅₆,13w₂₅₆), (−7w₂₅₆,11w₂₅₆), (−7w₂₅₆,9w₂₅₆),(−7w₂₅₆,7w₂₅₆), (−7w₂₅₆,5w₂₅₆), (−7w₂₅₆,3w₂₅₆), (−7w₂₅₆,w₂₅₆),

(−7w₂₅₆,−15w₂₅₆), (−7w₂₅₆,−13w₂₅₆), (−7w₂₅₆,−11w₂₅₆), (−7w₂₅₆,−9w₂₅₆),(−7w₂₅₆,−7w₂₅₆), (−7w₂₅₆,−5w₂₅₆), (−7w₂₅₆,−3w₂₅₆), (−7w₂₅₆,−w₂₅₆),

(−5w₂₅₆,15w₂₅₆), (−5w₂₅₆,13w₂₅₆), (−5w₂₅₆,11w₂₅₆), (−5w₂₅₆,9w₂₅₆),(−5w₂₅₆,7w₂₅₆), (−5w₂₅₆,5w₂₅₆), (−5w₂₅₆,3w₂₅₆), (−5w₂₅₆,w₂₅₆),

(−5w₂₅₆,−15w₂₅₆), (−5w₂₅₆,−13w₂₅₆), (−5w₂₅₆,−11w₂₅₆), (−5w₂₅₆,−9w₂₅₆),(−5w₂₅₆,−7w₂₅₆), (−5w₂₅₆,−5w₂₅₆), (−5w₂₅₆,−3w₂₅₆), (−5w₂₅₆,−w₂₅₆),

(−3w₂₅₆,15w₂₅₆), (−3w₂₅₆,13w₂₅₆), (−3w₂₅₆,11w₂₅₆), (−3w₂₅₆,9w₂₅₆),(−3w₂₅₆,7w₂₅₆), (−3w₂₅₆,5w₂₅₆), (−3w₂₅₆,3w₂₅₆), (−3w₂₅₆,w₂₅₆),

(−3w₂₅₆,−15w₂₅₆), (−3w₂₅₆,−13w₂₅₆), (−3w₂₅₆,−11w₂₅₆), (−3w₂₅₆,−9w₂₅₆),(−3w₂₅₆,−7w₂₅₆), (−3w₂₅₆,−5w₂₅₆), (−3w₂₅₆,−3w₂₅₆), (−3w₂₅₆,−w₂₅₆),

(−w₂₅₆,15w₂₅₆), (−w₂₅₆,13w₂₅₆), (−w₂₅₆,11w₂₅₆), (−w₂₅₆,9w₂₅₆),(−w₂₅₆,7w₂₅₆), (−w₂₅₆,5w₂₅₆), (−w₂₅₆,3w₂₅₆), (−w₂₅₆,w₂₅₆),

(−w₂₅₆,−15w₂₅₆), (−w₂₅₆,−w₂₅₆), (−w₂₅₆,−11w₂₅₆), (−w₂₅₆,−9w₂₅₆),(−w₂₅₆,−7w₂₅₆), (−w₂₅₆,−5w₂₅₆), (−w₂₅₆,−3w₂₅₆), (−w₂₅₆,−w₂₅₆)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, b5, b6, and b7. For example, in the case that the bitsto be transmitted is (b0, b1, b2, b3, b4, b5, b6, b7)=(0,0,0,0,0,0,0,0),the bits are mapped at signal point 2001 in FIG. 20 , and(I,Q)=(15w₂₅₆,15w₂₅₆) is obtained when I is an in-phase component whileQ is a quadrature component of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5, b6, b7),in-phase component I and quadrature component Q of the mapped basebandsignal are decided (during 256QAM modulation). FIG. 20 illustrates anexample of a relationship between the set of b0, b1, b2, b3, b4, b5, b6,and b7 (00000000 to 11111111) and the signal point coordinates. Values00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6, and b7are indicated immediately below 256 signal points included in 256QAM(the marks “◯” in FIG. 20 ) (15w₂₅₆,15w₂₅₆), (15w₂₅₆,13w₂₅₆),(15w₂₅₆,11w₂₅₆), (15w₂₅₆,9w₂₅₆), (15w₂₅₆,7w₂₅₆), (15w₂₅₆,5w₂₅₆),(15w₂₅₆,3w₂₅₆), (15w₂₅₆,w₂₅₆),

(15w₂₅₆,−15w₂₅₆), (15w₂₅₆,−13w₂₅₆), (15w₂₅₆,−11w₂₅₆), (15w₂₅₆,−9w₂₅₆),(15w₂₅₆,−7w₂₅₆), (15w₂₅₆,−5w₂₅₆), (15w₂₅₆,−3w₂₅₆), (15w₂₅₆,−w₂₅₆),

(13w₂₅₆,15w₂₅₆), (13w₂₅₆,13w₂₅₆), (13w₂₅₆,11w₂₅₆), (13w₂₅₆,9w₂₅₆),(13w₂₅₆,7w₂₅₆), (13w₂₅₆,5w₂₅₆), (13w₂₅₆,3w₂₅₆), (13w₂₅₆,w₂₅₆),

(13w₂₅₆,−15w₂₅₆), (13w₂₅₆,−13w₂₅₆), (13w₂₅₆,−11w₂₅₆), (13w₂₅₆,−9w₂₅₆),(13w₂₅₆,−7w₂₅₆), (13w₂₅₆,−5w₂₅₆), (13w₂₅₆,−3w₂₅₆), (13w₂₅₆,−w₂₅₆),

(11w₂₅₆,15w₂₅₆), (11w₂₅₆,13w₂₅₆), (11w₂₅₆,11w₂₅₆), (11w₂₅₆,9w₂₅₆),(11w₂₅₆,7w₂₅₆), (11w₂₅₆,5w₂₅₆), (11w₂₅₆,3w₂₅₆), (11w₂₅₆,w₂₅₆),

(11w₂₅₆,−15w₂₅₆), (11w₂₅₆,−13w₂₅₆), (11w₂₅₆,−11w₂₅₆), (11w₂₅₆,−9w₂₅₆),(11w₂₅₆,−7w₂₅₆), (11w₂₅₆,−5w₂₅₆), (11w₂₅₆,−3w₂₅₆), (11w₂₅₆,−w₂₅₆),

(9w₂₅₆,15w₂₅₆), (9w₂₅₆,13w₂₅₆), (9w₂₅₆,11w₂₅₆), (9w₂₅₆,9w₂₅₆),(9w₂₅₆,7w₂₅₆), (9w₂₅₆,5w₂₅₆), (9w₂₅₆,3w₂₅₆), (9w₂₅₆,w₂₅₆),

(9w₂₅₆,−15w₂₅₆), (9w₂₅₆,−13w₂₅₆), (9w₂₅₆,−11w₂₅₆), (9w₂₅₆,−9w₂₅₆),(9w₂₅₆,−7w₂₅₆), (9w₂₅₆,−5w₂₅₆), (9w₂₅₆,−3w₂₅₆), (9w₂₅₆,−w₂₅₆),

(7w₂₅₆,15w₂₅₆), (7w₂₅₆,13w₂₅₆), (7w₂₅₆,11w₂₅₆), (7w₂₅₆,9w₂₅₆),(7w₂₅₆,7w₂₅₆), (7w₂₅₆,5w₂₅₆), (7w₂₅₆,3w₂₅₆), (7w₂₅₆,w₂₅₆),

(7w₂₅₆,−15w₂₅₆), (7w₂₅₆,−13w₂₅₆), (7w₂₅₆,−11w₂₅₆), (7w₂₅₆,−9w₂₅₆),(7w₂₅₆,−7w₂₅₆), (7w₂₅₆,−5w₂₅₆), (7w₂₅₆,−3w₂₅₆), (7w₂₅₆,−w₂₅₆),

(5w₂₅₆,15w₂₅₆), (5w₂₅₆,13w₂₅₆), (5w₂₅₆,11w₂₅₆), (5w₂₅₆,9w₂₅₆),(5w₂₅₆,7w₂₅₆), (5w₂₅₆,5w₂₅₆), (5w₂₅₆,3w₂₅₆), (5w₂₅₆,w₂₅₆),

(5w₂₅₆,−15w₂₅₆), (5w₂₅₆,−13w₂₅₆), (5w₂₅₆,−11w₂₅₆), (5w₂₅₆,−9w₂₅₆),(5w₂₅₆,−7w₂₅₆), (5w₂₅₆,−5w₂₅₆), (5w₂₅₆,−3w₂₅₆), (5w₂₅₆,−w₂₅₆),

(3w₂₅₆,15w₂₅₆), (3w₂₅₆,13w₂₅₆), (3w₂₅₆,11w₂₅₆), (3w₂₅₆,9w₂₅₆),(3w₂₅₆,7w₂₅₆), (3w₂₅₆,5w₂₅₆), (3w₂₅₆,3w₂₅₆), (3w₂₅₆,w₂₅₆),

(3w₂₅₆,−15w₂₅₆), (3w₂₅₆,−13w₂₅₆), (3w₂₅₆,−11w₂₅₆), (3w₂₅₆,−9w₂₅₆),(3w₂₅₆,−7w₂₅₆), (3w₂₅₆,−5w₂₅₆), (3w₂₅₆,−3w₂₅₆), (3w₂₅₆,−w₂₅₆),

(w₂₅₆,15w₂₅₆), (w₂₅₆,13w₂₅₆), (w₂₅₆,11w₂₅₆), (w₂₅₆,9w₂₅₆), (w₂₅₆,7w₂₅₆),(w₂₅₆,5w₂₅₆), (w₂₅₆,3w₂₅₆), (w₂₅₆,w₂₅₆),

(w₂₅₆,−15w₂₅₆), (w₂₅₆,−13w₂₅₆), (w₂₅₆,−11w₂₅₆), (w₂₅₆,−9w₂₅₆),(w₂₅₆,−7w₂₅₆), (w₂₅₆,−5w₂₅₆), (w₂₅₆,−3w₂₅₆), (w₂₅₆,−w₂₅₆),

(−15w₂₅₆,15w₂₅₆), (−15w₂₅₆,13w₂₅₆), (−15w₂₅₆,11w₂₅₆), (−15w₂₅₆,9w₂₅₆),(−15w₂₅₆,7w₂₅₆), (−15w₂₅₆,5w₂₅₆), (−15w₂₅₆,3w₂₅₆), (−15w₂₅₆,w₂₅₆),

(−15w₂₅₆,−15w₂₅₆), (−15w₂₅₆,−13w₂₅₆), (−15w₂₅₆,−11w₂₅₆),(−15w₂₅₆,−9w₂₅₆), (−15w₂₅₆,−7w₂₅₆), (−15w₂₅₆,−5w₂₅₆), (−15w₂₅₆,−3w₂₅₆),(−15w₂₅₆,−w₂₅₆),

(−13w₂₅₆,15w₂₅₆), (−13w₂₅₆,13w₂₅₆), (−13w₂₅₆,11w₂₅₆), (−13w₂₅₆,9w₂₅₆),(−13w₂₅₆,7w₂₅₆), (−13w₂₅₆,5w₂₅₆), (−13w₂₅₆,3w₂₅₆), (−13w₂₅₆,w₂₅₆),

(−13w₂₅₆,−15w₂₅₆), (−13w₂₅₆,−13w₂₅₆), (−13w₂₅₆,−11w₂₅₆),(−13w₂₅₆,−9w₂₅₆), (−13w₂₅₆,−7w₂₅₆), (−13w₂₅₆,−5w₂₅₆), (−13w₂₅₆,−3w₂₅₆),(−13w₂₅₆,−w₂₅₆),

(−11w₂₅₆,15w₂₅₆), (−11w₂₅₆,13w₂₅₆), (−11w₂₅₆,11w₂₅₆), (−11w₂₅₆,9w₂₅₆),(−11w₂₅₆,7w₂₅₆), (−11w₂₅₆,5w₂₅₆), (−11w₂₅₆,3w₂₅₆), (−11w₂₅₆,w₂₅₆),

(−11w₂₅₆,−15w₂₅₆), (−11w₂₅₆,−13w₂₅₆), (−11w₂₅₆,−11w₂₅₆),(−11w₂₅₆,−9w₂₅₆), (−11w₂₅₆,−7w₂₅₆), (−11w₂₅₆,−5w₂₅₆), (−11w₂₅₆,−3w₂₅₆),(−11w₂₅₆,−w₂₅₆),

(−9w₂₅₆,15w₂₅₆), (−9w₂₅₆,13w₂₅₆), (−9w₂₅₆,11w₂₅₆), (−9w₂₅₆,9w₂₅₆),(−9w₂₅₆,7w₂₅₆), (−9w₂₅₆,5w₂₅₆), (−9w₂₅₆,3w₂₅₆), (−9w₂₅₆,w₂₅₆),

(−9w₂₅₆,−15w₂₅₆), (−9w₂₅₆,−13w₂₅₆), (−9w₂₅₆,−11w₂₅₆), (−9w₂₅₆,−9w₂₅₆),(−9w₂₅₆,−7w₂₅₆), (−9w₂₅₆,−5w₂₅₆), (−9w₂₅₆,−3w₂₅₆), (−9w₂₅₆,−w₂₅₆),

(−7w₂₅₆,15w₂₅₆), (−7w₂₅₆,13w₂₅₆), (−7w₂₅₆,11w₂₅₆), (−7w₂₅₆,9w₂₅₆),(−7w₂₅₆,7w₂₅₆), (−7w₂₅₆,5w₂₅₆), (−7w₂₅₆,3w₂₅₆), (−7w₂₅₆,w₂₅₆),

(−7w₂₅₆,−15w₂₅₆), (−7w₂₅₆,−13w₂₅₆), (−7w₂₅₆,−11w₂₅₆), (−7w₂₅₆,−9w₂₅₆),(−7w₂₅₆,−7w₂₅₆), (−7w₂₅₆,−5w₂₅₆), (−7w₂₅₆,−3w₂₅₆), (−7w₂₅₆,−w₂₅₆),

(−5w₂₅₆,15w₂₅₆), (−5w₂₅₆,13w₂₅₆), (−5w₂₅₆,11w₂₅₆), (−5w₂₅₆,9w₂₅₆),(−5w₂₅₆,7w₂₅₆), (−5w₂₅₆,5w₂₅₆), (−5w₂₅₆,3w₂₅₆), (−5w₂₅₆,w₂₅₆),

(−5w₂₅₆,−15w₂₅₆), (−5w₂₅₆,−13w₂₅₆), (−5w₂₅₆,−11w₂₅₆), (−5w₂₅₆,−9w₂₅₆),(−5w₂₅₆,−7w₂₅₆), (−5w₂₅₆,−5w₂₅₆), (−5w₂₅₆,−3w₂₅₆), (−5w₂₅₆,−w₂₅₆),

(−3w₂₅₆,15w₂₅₆), (−3w₂₅₆,13w₂₅₆), (−3w₂₅₆,11w₂₅₆), (−3w₂₅₆,9w₂₅₆),(−3w₂₅₆,7w₂₅₆), (−3w₂₅₆,5w₂₅₆), (−3w₂₅₆,3w₂₅₆), (−3w₂₅₆,w₂₅₆),

(−3w₂₅₆,−15w₂₅₆), (−3w₂₅₆,−13w₂₅₆), (−3w₂₅₆,−11w₂₅₆), (−3w₂₅₆,−9w₂₅₆),(−3w₂₅₆,−7w₂₅₆), (−3w₂₅₆,−5w₂₅₆), (−3w₂₅₆,−3w₂₅₆), (−3w₂₅₆,−w₂₅₆),

(−w₂₅₆,15w₂₅₆), (−w₂₅₆,13w₂₅₆), (−w₂₅₆,11w₂₅₆), (−w₂₅₆,9w₂₅₆),(−w₂₅₆,7w₂₅₆), (−w₂₅₆,5w₂₅₆), (−w₂₅₆,3w₂₅₆), (−w₂₅₆,w₂₅₆),

(−w₂₅₆,−15w₂₅₆), (−w₂₅₆,−w₂₅₆), (−w₂₅₆,−11w₂₅₆), (−w₂₅₆,−9w₂₅₆),(−w₂₅₆,−7w₂₅₆), (−w₂₅₆,−5w₂₅₆), (−w₂₅₆,−3w₂₅₆), (−w₂₅₆,−w₂₅₆).Respective coordinates of the signal points (“◯”) immediately above thevalues 00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6,and b7 in the I-Q plane serve as in-phase component I and quadraturecomponent Q of the mapped baseband signal. The relationship between theset of b0, b1, b2, b3, b4, b5, b6, and b7 (00000000 to 11111111) and thesignal point coordinates during 256QAM modulation is not limited to thatin FIG. 20 . A complex value of in-phase component I and quadraturecomponent Q of the mapped baseband signal (during 256QAM modulation)serves as a baseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7 ).

In this case, the modulation scheme of baseband signal 505A (s₁(t)(s₁(i))) is set to 64QAM while modulation scheme of baseband signal 505B(s₂(t) (s₂(i))) is set to 256QAM in FIG. 5 to FIG. 7 . The configurationof the precoding matrix will be described below.

At this point, generally average power of baseband signal 505A (s₁(t)and (s₁(i))) and average power of baseband signal 505B (s₂(t) and(s₂(i))), which are of the output of mapper 504 in FIGS. 5 to 7 , areequalized to each other. Accordingly, the following relationalexpression holds with respect to coefficient w₆₄ of the 64QAM mappingmethod and coefficient w₂₅₆ of the 256QAM mapping method.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 192} \right\rbrack & \; \\{w_{64} = \frac{z}{\sqrt{42}}} & ({S153}) \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 193} \right\rbrack & \; \\{w_{256} = \frac{z}{\sqrt{170}}} & ({S154})\end{matrix}$

In equations (S153) and (S154), it is assumed that z is a real numberlarger than 0. When the calculations are performed in <1> to <5>,

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

the configuration of precoding matrix F

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 194} \right\rbrack & \; \\{F = \begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}} & ({S155})\end{matrix}$

will be described in detail below ((Example 3-1) to (Example 3-8)).

Example 3-1

For one of <1> to <5>, precoding matrix F is set to one of the followingequations.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 195} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S156})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 196} \right\rbrack & \; \\{{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}}{or}} & {{Formula}\mspace{14mu}({S157})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 197} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S158})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 198} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\;{\pi 0}}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S159})}\end{matrix}$

In equations (S156), (S157), (S158), and (S159), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 199} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}}}{or}} & {{Formula}\mspace{14mu}({S160})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 200} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}}} & {{Formula}\mspace{14mu}({S161})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 201} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8} \times e^{j\frac{\pi}{2}}}}{or}} & {{Formula}\mspace{14mu}({S162})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 202} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}({S163})}\end{matrix}$

The modulation scheme of baseband signal 505A (s₁(t) (s₁(i))) is set to64QAM while modulation scheme of baseband signal 505B (s₂(t) (s₂(i))) isset to 256QAM. Accordingly, the precoding (and the phase change and thepower change) is performed to transmit the modulated signal from eachantenna as described above, the total number of bits transmitted usingsymbols transmitted from antenna 808A and 808B in FIG. 8 at the (unit)time of time u and frequency (carrier) v is 14 bits that are of a sum of6 bits (for the use of 64QAM) and 8 bits (for the use of 256QAM).

Assuming that b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) andb_(5,64) are input bits for the purpose of the 64QAM mapping, and thatb_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), and b_(7,256) are input bits for the purpose of the 256QAMmapping, even if value α in any one of equations (S160), (S161), (S162),and (S163) is used, in signal z₁(t) (z₁(i)),

the signal point at which (b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64) b_(5,64), b_(0,256), b_(1,256), b_(2,256), b_(3,256),b_(4,256), b_(5,256), b_(6,256), b_(7,256)) corresponds to(0,0,0,0,0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64), b_(0,256), b_(1,256),b_(2,256), b_(3,256), b_(4,256), b_(5,256), b_(6,256), b_(7,256))corresponds to (1,1,1,1,1,1,1,1,1,1,1,1,1,1) exist in the I-Q plane,similarly, in signal z₂(t) (z₂(i)),the Signal point at Which (b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64) b_(5,64), b_(0,256), b_(1,256), b_(2,256), b_(3,256),b_(4,256), b_(5,256), b_(6,256), b_(7,256)) corresponds to(0,0,0,0,0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64), b_(0,256), b_(1,256),b_(2,256), b_(3,256), b_(4,256), b_(5,256), b_(6,256), b_(7,256))corresponds to (1,1,1,1,1,1,1,1,1,1,1,1,1,1) exist in the I-Q plane.

In the above description, with respect to signal z₁(t) (z₁(i)) inequations (s2), (S3), (S4), (S5), and (S8), equations (S160) to (S163)are considered as value α with which the receiver obtains the good datareception quality. This point will be described below.

In signal z₁(t) (z₁(i)),

the Signal point at Which (b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64) b_(5,64), b_(0,256), b_(1,256), b_(2,256), b_(3,256),b_(4,256), b_(5,256), b_(6,256), b_(7,256)) corresponds to(0,0,0,0,0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64), b_(0,256), b_(1,256),b_(2,256), b_(3,256), b_(4,256), b_(5,256), b_(6,256), b_(7,256))corresponds to (1,1,1,1,1,1,1,1,1,1,1,1,1,1) exist in the I-Q plane, andit is desirable that 2¹⁴=16384 signal points exist in the I-Q planewhile not overlapping one another.

This is attributed to the following fact. That is, the receiver performsthe detection and the error correction decoding using signal z₁(t)(z₁(i)) in the case that a modulated signal transmitted from the antennafor transmitting signal z₂(t) (z₂(i)) does not reach the receiver, andit is necessary at that time that the 16384 signal points exist in theI-Q plane while not overlapping one another in order that the receiverobtains the high data reception quality.

In the case that precoding matrix F is set to one of equations (S156),(S157), (S158), and (S159), and that α is set to one of equations(S160), (S161), (S162), and (S163), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, the arrangement of the signal points existing in afirst quadrant is obtained as illustrated in FIG. 21 , the arrangementof the signal points existing in a second quadrant is obtained asillustrated in FIG. 22 , the arrangement of the signal points existingin a third quadrant is obtained as illustrated in FIG. 23 , and thearrangement of the signal points existing in a fourth quadrant isobtained as illustrated in FIG. 24 . In FIGS. 21, 22, 23, and 24 , ahorizontal axis indicates I, and a vertical axis indicates Q, a mark “●”indicates a signal point, and a mark “Δ” indicates origin (0).

As can be seen from FIGS. 21, 22, 23, and 24 , the 16384 signal pointsexist while not overlapping one another in the I-Q plane. On the I-Qplane, Euclidean distances between closest signal points are equal inthe 16380 signal points of the 16384 signal points except for therightmost and uppermost point in FIG. 21 , the rightmost and lowermostpoint in FIG. 24 , the leftmost and uppermost point in FIG. 22 , and theleftmost and lowermost point in FIG. 23 . Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S156),(S157), (S158), and (S159), and that α is set to one of equations(S160), (S161), (S162), and (S163), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, the arrangement of the signal points existing inthe first quadrant is obtained as illustrated in FIG. 25 , thearrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 26 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.27 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 28 . In FIGS. 25, 26, 27,and 28 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 25, 26, 27, and 28 , the 16384 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 16384signal points in FIGS. 21, 22, 23, and 24 , and that D₂ is a minimumEuclidean distance at the 16384 signal points in FIGS. 25, 26, 27, and28 . D₁>D₂ holds. Accordingly, from configuration example R1, it isnecessary that |Q₁|>|Q₂| holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 3-2

Then, equations (S153) and (S154) hold with respect to coefficient w₆₄of the 64QAM mapping method and coefficient w₂₅₆ of the 256QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 203} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S164})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 204} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S165})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 205} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S166})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 206} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S167})}\end{matrix} & \;\end{matrix}$

In equations (S164) and (S166), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 207} \right\rbrack & \; \\{{{\theta = {\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}} \right)}}{or}{\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}} \right)} + {2n\;{\pi({radian})}}}{or}} & {{Formula}\mspace{14mu}({S168})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 208} \right\rbrack & \; \\{{{\theta = {\pi + {\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}} \right)}}}{or}\pi + {\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}} \right)} + {2n\;{\pi({radian})}}}{or}} & {{Formula}\mspace{14mu}({S169})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 209} \right\rbrack & \; \\{{{\theta = {\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}} \right)}}{or}{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}} \right)} + {2n\;{\pi({radian})}}}{or}} & {{Formula}\mspace{14mu}({S170})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 210} \right\rbrack & \; \\{{\theta = {\pi + {\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}} \right)}}}{or}{\pi + {\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S171})}\end{matrix} & \;\end{matrix}$

In equations (S168), (S169), (S170), and (S171), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 2111} \right\rbrack & \; \\{{{- \frac{\pi}{2}}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}({radian})}} & {{Formula}\mspace{14mu}({S172})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S164),(S165), (S166), and (S167), and that θ is set to one of equations(S168), (S169), (S170), and (S171), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 21 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 22 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.23 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 24 . In FIGS. 21,22, 23, and24 , a horizontal axis indicates I, and a vertical axis indicates Q, amark “●” indicates a signal point, and a mark “Δ” indicates origin (0).

As can be seen from FIGS. 21, 22, 23, and 24 , the 16384 signal pointsexist while not overlapping one another in the I-Q plane. On the I-Qplane, Euclidean distances between closest signal points are equal inthe 16380 signal points of the 16384 signal points except for therightmost and uppermost point in FIG. 21 , the rightmost and lowermostpoint in FIG. 24 , the leftmost and uppermost point in FIG. 22 , and theleftmost and lowermost point in FIG. 23 . Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S164),(S165), (S166), and (S167), and that θ is set to one of equations(S168), (S169), (S170), and (S171), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 25 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 26 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.27 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 28 . In FIGS. 25, 26, 27,and 28 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 25, 26, 27, and 28 , the 16384 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 16384signal points in FIGS. 21, 22, 23, and 24 , and that D₂ is a minimumEuclidean distance at the 16384 signal points in FIGS. 25, 26, 27, and28 . D₁>D₂ holds. Accordingly, from configuration example R1, it isnecessary that |Q₁|>|Q₂| holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 3-3

Equations (S153) and (S154) hold with respect to coefficient w₆₄ of the64QAM mapping method and coefficient w₂₅₆ of the 256QAM mapping method,and precoding matrix F is set to one of equations (S173), (S174),(S175), and (S176) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 212} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S173})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 213} \right\rbrack & \; \\{{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}}{or}} & {{Formula}\mspace{14mu}({S174})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 214} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S175})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 215} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S176})}\end{matrix}$

In equations (S173), (S174), (S175), and (S176), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 216} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9}}}{or}} & {{Formula}\mspace{14mu}({S177})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 217} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{8}{9}}} & {{Formula}\mspace{14mu}({S178})}\end{matrix} & \;\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 218} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9} \times e^{j\frac{\pi}{2}}}}{or}} & {{Formula}\mspace{14mu}({S179})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 219} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}({S180})}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S173),(S174), (S175), and (S176), and that α is set to one of equations(S177), (S178), (S179), and (S180), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 29 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 30 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.31 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 32 . In FIGS. 29, 30, 31,and 32 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 29, 30, 31, and 32 , the 16384 signal pointsexist while not overlapping one another. On the I-Q plane, Euclideandistances between closest signal points are equal in the 16380 signalpoints of the 16384 signal points except for the rightmost and uppermostpoint in FIG. 29 , the rightmost and lowermost point in FIG. 32 , theleftmost and uppermost point in FIG. 30 , and the leftmost and lowermostpoint in FIG. 31 . Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S173),(S174), (S175), and (S176), and that α is set to one of equations(S177), (S178), (S179), and (S180), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 33 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 34 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.35 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 36 . In FIGS. 33, 34, 35,and 36 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 33, 34, 35, and 36 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 16384signal points in FIGS. 29, 30, 31, and 32 , and that D₂ is a minimumEuclidean distance at the 16384 signal points in FIGS. 33, 34, 35, and36 . D₁>D₂ holds. Accordingly, from configuration example R1, it isnecessary that |Q₁|>|Q₂| holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 3-4

Then, equations (S153) and (S154) hold with respect to coefficient w₆₄of the 64QAM mapping method and coefficient w₂₅₆ of the 256QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 220} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S181})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 221} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S182})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 222} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S183})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 223} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S184})}\end{matrix}$

In equations (S181) and (S183), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 224} \right\rbrack & \; \\{{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{170}}{42} \times \frac{8}{9}} \right)}} + {2\; n\;\pi\mspace{14mu}({radian})}}}\;{or}} & {{Formula}\mspace{14mu}({S185})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 225} \right\rbrack & \; \\{{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{170}}{42} \times \frac{8}{9}} \right)} + {2\; n\;\pi\mspace{14mu}({radian})}}}\;{or}} & {{Formula}\mspace{14mu}({S186})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 226} \right\rbrack & \; \\{{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{42}} \times \frac{8}{9}} \right)}} + {2\; n\;\pi\mspace{14mu}({radian})}}}\;{or}} & {{Formula}\mspace{14mu}({S187})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 227} \right\rbrack & \; \\{{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{170}}{42}} \times \frac{8}{9}} \right)} + {2\; n\;\pi\mspace{14mu}({radian})}}}\;} & {{Formula}\mspace{14mu}({S188})}\end{matrix}$

In equations (S185), (S186), (S187), and (S188), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 228} \right\rbrack & \; \\{{{- \frac{\pi}{2}}\mspace{11mu}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi\;}{2}\mspace{11mu}({radian})}} & {{Formula}\mspace{14mu}({S189})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S181),(S182), (S183), and (S184), and that θ is set to one of equations(S185), (S186), (S187), and (S188), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 29 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 30 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.31 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 32 . In FIGS. 29, 30, 31 ,and 32, a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 29, 30, 31, and 32 , the 16384 signal pointsexist while not overlapping one another in the I-Q plane. On the I-Qplane, Euclidean distances between closest signal points are equal inthe 16380 signal points of the 16384 signal points except for therightmost and uppermost point in FIG. 29 , the rightmost and lowermostpoint in FIG. 32 , the leftmost and uppermost point in FIG. 30 , and theleftmost and lowermost point in FIG. 31 . Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S181),(S182), (S183), and (S184), and that θ is set to one of equations(S185), (S186), (S187), and (S188), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 33 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 34 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.35 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 36 . In FIGS. 33, 34, 35,and 36 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 33, 34, 35, and 36 , the 16384 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 16384signal points in FIGS. 29, 30, 31, and 32 , and that D₂ is a minimumEuclidean distance at the 16384 signal points in FIGS. 33, 34, 35, and36 . D₁>D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁>Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 3-5

Equations (S153) and (S154) hold with respect to coefficient w₆₄ of the64QAM mapping method and coefficient w₂₅₆ of the 256QAM mapping method,and precoding matrix F is set to one of equations (S173), (S174),(S175), and (S176) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 229} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S190})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 230} \right\rbrack & \; \\{{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}}{or}} & {{Formula}\mspace{14mu}({S191})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 231} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S192})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 232} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S193})}\end{matrix}$

In equations (S190), (S191), (S192), and (S193), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 233} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{42}}{170} \times \frac{9}{8}}}{or}} & {{Formula}\mspace{14mu}({S194})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 234} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}}} & {{Formula}\mspace{14mu}({S195})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 235} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8} \times e^{j\frac{\pi}{2}}}}{or}} & {{Formula}\mspace{14mu}({S196})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 236} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8} \times e^{j\frac{3\;\pi}{2}}}} & {{Formula}\mspace{14mu}({S197})}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S190),(S191), (S192), and (S193), and that α is set to one of equations(S194), (S195), (S196), and (S197), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q the I-Q plane, similarly the arrangement of the signalpoints existing in the first quadrant is obtained as illustrated in FIG.37 , the arrangement of the signal points existing in the secondquadrant is obtained as illustrated in FIG. 38 , the arrangement of thesignal points existing in the third quadrant is obtained as illustratedin FIG. 39 , and the arrangement of the signal points existing in thefourth quadrant is obtained as illustrated in FIG. 40 . In FIGS. 37, 38,39, and 40 , a horizontal axis indicates I, and a vertical axisindicates Q, a mark “●” indicates a signal point, and a mark “Δ”indicates origin (0).

As can be seen from FIGS. 37, 38, 39, and 40 , the 16384 signal pointsexist while not overlapping one another. On the I-Q plane, Euclideandistances between closest signal points are equal in the 16380 signalpoints of the 16384 signal points except for the rightmost and uppermostpoint in FIG. 37 , the rightmost and lowermost point in FIG. 40 , theleftmost and uppermost point in FIG. 38 , and the leftmost and lowermostpoint in FIG. 39 . Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S190),(S191), (S192), and (S193), and that α is set to one of equations(S194), (S195), (S196), and (S197), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 41 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 42 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.43 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 44 . In FIGS. 41,42, 43, and44 , a horizontal axis indicates I, and a vertical axis indicates Q, amark “●” indicates a signal point, and a mark “Δ” indicates origin (0).

As can be seen from FIGS. 41,42, 43, and 44 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 16384signal points in FIGS. 37, 38, 39, and 40 , and that D₁ is a minimumEuclidean distance at the 16384 signal points in FIGS. 41, 42, 43, and44 . D₁<D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁<Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 3-6

Then, equations (S153) and (S154) hold with respect to coefficient w₆₄of the 64QAM mapping method and coefficient w₂₅₆ of the 256QAM mappingmethod, and precoding matrix F is set to one of equations (S22), (S23),(S24), and (S25) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 237} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{11mu}\theta} & {\beta \times \sin\mspace{11mu}\theta} \\{\beta \times \sin\mspace{11mu}\theta} & {{- \beta} \times \cos\mspace{11mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S198})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 238} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\mspace{11mu}\theta} & {\sin\mspace{11mu}\theta} \\{\sin\mspace{11mu}\theta} & {{- \cos}\mspace{11mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S199})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 239} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{11mu}\theta} & {{- \beta} \times \sin\mspace{11mu}\theta} \\{\beta \times \sin\mspace{11mu}\theta} & {{- \beta} \times \cos\mspace{11mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S200})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 240} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\mspace{11mu}\theta} & {{- \sin}\mspace{11mu}\theta} \\{\sin\mspace{11mu}\theta} & {\cos\mspace{11mu}\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S201})}\end{matrix}$

In equations (S198) and equation (S200), β may be either a real numberor an imaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 241} \right\rbrack & \; \\{{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{42}}{170} \times \frac{9}{8}} \right)}} + {2n\;\pi\mspace{11mu}({radian})}}}{or}} & {{Formula}\mspace{14mu}({S202})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 242} \right\rbrack & \; \\{{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8}} \right)} + {2n\;\pi\mspace{11mu}({radian})}}}{or}} & {{Formula}\mspace{14mu}({S203})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 243} \right\rbrack & \; \\{{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}} \right)}} + {2n\;\pi\mspace{11mu}({radian})}}}{or}} & {{Formula}\mspace{14mu}({S204})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 244} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}} \right)} + {2n\;\pi\mspace{11mu}({radian})}}} & {{Formula}\mspace{14mu}({S205})}\end{matrix}$

In equations (S202), (S203), (S204), and (S205), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 245} \right\rbrack & \; \\{{{- \frac{\pi}{2}}\mspace{11mu}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}\mspace{11mu}({radian})}} & {{Formula}\mspace{14mu}({S206})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S198),(S199), (S200), and (S201), and that θ is set to one of equations(S202), (S203), (S204), and (S205), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 37 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 38 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.39 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 40 . In FIGS. 37, 38, 39,and 40 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 37, 38, 39, and 40 , the 16384 signal pointsexist while not overlapping one another. On the I-Q plane, Euclideandistances between closest signal points are equal in the 16380 signalpoints of the 16384 signal points except for the rightmost and uppermostpoint in FIG. 37 , the rightmost and lowermost point in FIG. 40 , theleftmost and uppermost point in FIG. 38 , and the leftmost and lowermostpoint in FIG. 39 . Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S198),(S199), (S200), and (S201), and that θ is set to one of equations(S202), (S203), (S204), and (S205), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 41 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 42 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.43 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 44 . In FIGS. 41,42, 43, and44 , a horizontal axis indicates I, and a vertical axis indicates Q, amark “●” indicates a signal point, and a mark “Δ” indicates origin (0).

As can be seen from FIGS. 41,42, 43, and 44 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 16384signal points in FIGS. 37, 38, 39, and 40 , and that D₁ is a minimumEuclidean distance at the 16384 signal points in FIGS. 41, 42, 43, and44 . D₁<D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁<Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 3-7

Equations (S153) and (S154) hold with respect to coefficient w₆₄ of the64QAM mapping method and coefficient w₂₅₆ of the 256QAM mapping method,and precoding matrix F is set to one of equations (S173), (S174),(S175), and (S176) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 246} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S207})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 247} \right\rbrack & \; \\{{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}}{or}} & {{Formula}\mspace{14mu}({S208})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 248} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S209})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 249} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S210})}\end{matrix}$

In equations (S207), (S208), (S209), and (S210), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 250} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{8}{9}}}{or}} & {{Formula}\mspace{14mu}({S211})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 251} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{42}}{170}} \times \frac{8}{9}}} & {{Formula}\mspace{14mu}({S212})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 252} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{42}}{170} \times \frac{8}{9} \times e^{j\frac{\pi}{2}}}}{or}} & {{Formula}\mspace{14mu}({S213})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 253} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{170} \times \frac{8}{9} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}({S214})}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S207),(S208), (S209), and (S210), and that α is set to one of equations(S211), (S212), (S213), and (S214), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 45 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 46 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.47 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 48 . In FIGS. 45, 46, 47,and 48 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 45, 46, 47, and 48 , the 16384 signal pointsexist while not overlapping one another. On the I-Q plane, Euclideandistances between closest signal points are equal in the 16380 signalpoints of the 16384 signal points except for the rightmost and uppermostpoint in FIG. 45 , the rightmost and lowermost point in FIG. 48 , theleftmost and uppermost point in FIG. 46 , and the leftmost and lowermostpoint in FIG. 47 . Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S207),(S208), (S209), and (S210), and that α is set to one of equations(S211), (S212), (S213), and (S214), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 49 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 50 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.51 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 52 . In FIGS. 49, 50, 51,and 52 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 49, 50, 51, and 52 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 16384signal points in FIGS. 45, 46, 47, and 48 , and that D₁ is a minimumEuclidean distance at the 16384 signal points in FIGS. 49, 50, 51, and52 . D₁<D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁<Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 3-8

Equations (S153) and (S154) hold with respect to coefficient w₆₄ of the64QAM mapping method and coefficient w₂₅₆ of the 256QAM mapping method,and precoding matrix F is set to one of equations (S173), (S174),(S175), and (S176) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 254} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{11mu}\theta} & {\beta \times \sin\mspace{11mu}\theta} \\{\beta \times \sin\mspace{11mu}\theta} & {{- \beta} \times \cos\mspace{11mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S215})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 255} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\mspace{11mu}\theta} & {\sin\mspace{11mu}\theta} \\{\sin\mspace{11mu}\theta} & {{- \cos}\mspace{11mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S216})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 256} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{11mu}\theta} & {{- \beta} \times \sin\mspace{11mu}\theta} \\{\beta \times \sin\mspace{11mu}\theta} & {\beta \times \cos\mspace{11mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}({S217})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 257} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\mspace{11mu}\theta} & {{- \sin}\mspace{11mu}\theta} \\{\sin\mspace{11mu}\theta} & {\cos\mspace{11mu}\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S218})}\end{matrix}$

In equations (S215) and (S217), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 258} \right\rbrack & \; \\{{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{42}}{170} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{42}}{170} \times \frac{8}{9}} \right)}} + {2n\;\pi\mspace{11mu}({radian})}}}{or}} & \left. {{Formula}\mspace{14mu}{S219}} \right) \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 259} \right\rbrack & \; \\{{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{8}{9}} \right)} + {2n\;\pi\mspace{11mu}({radian})}}}{or}} & {{Formula}\mspace{14mu}({S220})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 260} \right\rbrack & \; \\{{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{42}}{170} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{42}}{170} \times \frac{8}{9}} \right)}} + {2n\;\pi\mspace{11mu}({radian})}}}{or}} & {{Formula}\mspace{14mu}({S221})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 261} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{170}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{42}}{170}} \times \frac{8}{9}} \right)} + {2n\;\pi\mspace{11mu}({radian})}}} & {{Formula}\mspace{14mu}({S222})}\end{matrix}$

In equations (S219), (S220), (S221), and (S222), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 262} \right\rbrack & \; \\{{{- \frac{\pi}{2}}\mspace{11mu}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}\mspace{11mu}({radian})}} & {{Formula}\mspace{14mu}({S223})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S215),(S216), (S217), and (S218), and that θ is set to one of equations(S219), (S220), (S221), and (S222), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 45 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 46 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.47 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 48 . In FIGS. 45, 46, 47,and 48 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 45, 46, 47, and 48 , the 16384 signal pointsexist while not overlapping one another. On the I-Q plane, Euclideandistances between closest signal points are equal in the 16380 signalpoints of the 16384 signal points except for the rightmost and uppermostpoint in FIG. 45 , the rightmost and lowermost point in FIG. 48 , theleftmost and uppermost point in FIG. 46 , and the leftmost and lowermostpoint in FIG. 47 . Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S215),(S216), (S217), and (S218), and that θ is set to one of equations(S219), (S220), (S221), and (S222), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 49 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 50 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.51 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 52 . In FIGS. 49, 50, 51,and 52 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 49, 50, 51, and 52 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 16384signal points in FIGS. 45, 46, 47, and 48 , and that D₁ is a minimumEuclidean distance at the 16384 signal points in FIGS. 49, 50, 51, and52 . D₁<D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁<Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 3-Supplement

Values α and θ having the possibility of achieving the high datareception quality are illustrated in (Example 3-1) to (Example 3-8).However, even if values α and θ are not those in (Example 3-1) to(Example 3-8), sometimes the high data reception quality is obtained bysatisfying the condition of configuration example R1.

Example 4

In mapper 504 of FIGS. 5 to 7 , the modulation scheme for obtainings₁(t) (s₁(i)) is set to 256QAM while the modulation scheme for obtainings₂(t) (s₂(i)) is set to 64QAM. An example of conditions associated withthe configuration and power change of precoding matrix (F) when theprecoding and/or the power change is performed on, for example, one ofequations (s2), (S3), (S4), (S5), and (S8) will be described below.

The 64QAM mapping method will be described below. FIG. 11 illustrates anarrangement example of 64QAM signal points in the I-Q plane. In FIG. 11, 64 marks “◯” indicate 64QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

64 64QAM 0069signal points (indicated by the marks “◯” in FIG. 11 ) inthe I-Q plane are obtained as follows. (w₆₄ is a real number larger than0)

(7w₆₄,7w₆₄), (7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄),(7w₆₄,−3w₆₄), (7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄)

(−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄), (−w₆₄,w₆₄), (−w₆₄,−w₆₄),(−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄,−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, in the case that the bits to betransmitted is (b0, b1, b2, b3, b4, b5)=(0,0,0,0,0,0), the bits aremapped at signal point 1101 in FIG. 11 , and (I,Q)=(7w₆₄,7w₆₄) isobtained when I is an in-phase component while Q is a quadraturecomponent of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 11 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to 111111 of theset of b0, b1, b2, b3, b4, and b5 are indicated immediately below 64signal points included in 64QAM (the marks “◯” in FIG. 11 ) (7w₆₄,7w₆₄),(7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄), (7w₆₄,−3w₆₄),(7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄)

(−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄), (−w₆₄,w₆₄), (−w₆₄,−w₆₄),(−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄,−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w_(64J)-7w₆₄). Respective coordinatesof the signal points (“◯”) immediately above the values 000000 to 111111of the set of b0, b1, b2, b3, b4, and b5 in the I-Q plane serve asin-phase component I and quadrature component Q of the mapped basebandsignal. The relationship between the set of b0, b1, b2, b3, b4, and b5(000000 to 111111) and the signal point coordinates during 64QAMmodulation is not limited to that in FIG. 11 . A complex value ofin-phase component I and quadrature component Q of the mapped basebandsignal (during 64QAM modulation) serves as a baseband signal (s₁(t) ors₂(t) in FIGS. 5 to 7 ).

The 256QAM mapping method will be described below. FIG. 20 illustratesan arrangement example of 256QAM signal points in the I-Q plane. In FIG.20 , 256 marks “◯” indicate the 256QAM signal points.

In the I-Q plane, 256 signal points included in 256QAM (indicated by themarks “◯” in FIG. 20 ) are obtained as follows. (w₂₅₆ is a real numberlarger than 0)

(15w₂₅₆,15w₂₅₆), (15w₂₅₆,13w₂₅₆), (15w₂₅₆,11w₂₅₆), (15w₂₅₆,9w₂₅₆),(15w₂₅₆,7w₂₅₆), (15w₂₅₆,5w₂₅₆), (15w₂₅₆,3w₂₅₆), (15w₂₅₆,w₂₅₆),

(15w₂₅₆,−15w₂₅₆), (15w₂₅₆,−13w₂₅₆), (15w₂₅₆,−11w₂₅₆), (15w₂₅₆,−9w₂₅₆),(15w₂₅₆,−7w₂₅₆), (15w₂₅₆,−5w₂₅₆), (15w₂₅₆,−3w₂₅₆), (15w₂₅₆,−w₂₅₆),

(13w₂₅₆,15w₂₅₆), (13w₂₅₆,13w₂₅₆), (13w₂₅₆,11w₂₅₆), (13w₂₅₆,9w₂₅₆),(13w₂₅₆,7w₂₅₆), (13w₂₅₆,5w₂₅₆), (13w₂₅₆,3w₂₅₆), (13w₂₅₆,w₂₅₆),

(13w₂₅₆,−15w₂₅₆), (13w₂₅₆,−13w₂₅₆), (13w₂₅₆,−11w₂₅₆), (13w₂₅₆,−9w₂₅₆),(13w₂₅₆,−7w₂₅₆), (13w₂₅₆,−5w₂₅₆), (13w₂₅₆,−3w₂₅₆), (13w₂₅₆,−w₂₅₆),

(11w₂₅₆,15w₂₅₆), (11w₂₅₆,13w₂₅₆), (11w₂₅₆,11w₂₅₆), (11w₂₅₆,9w₂₅₆),(11w₂₅₆,7w₂₅₆), (11w₂₅₆,5w₂₅₆), (11w₂₅₆,3w₂₅₆), (11w₂₅₆,w₂₅₆),

(11w₂₅₆,−15w₂₅₆), (11w₂₅₆,−13w₂₅₆), (11w₂₅₆,−11w₂₅₆), (11w₂₅₆,−9w₂₅₆),(11w₂₅₆,−7w₂₅₆), (11w₂₅₆,−5w₂₅₆), (11w₂₅₆,−3w₂₅₆), (11w₂₅₆,−w₂₅₆),

(9w₂₅₆,15w₂₅₆), (9w₂₅₆,13w₂₅₆), (9w₂₅₆,11w₂₅₆), (9w₂₅₆,9w₂₅₆),(9w₂₅₆,7w₂₅₆), (9w₂₅₆,5w₂₅₆), (9w₂₅₆,3w₂₅₆), (9w₂₅₆,w₂₅₆),

(9w₂₅₆,−15w₂₅₆), (9w₂₅₆,−13w₂₅₆), (9w₂₅₆,−11w₂₅₆), (9w₂₅₆,−9w₂₅₆),(9w₂₅₆,−7w₂₅₆), (9w₂₅₆,−5w₂₅₆), (9w₂₅₆,−3w₂₅₆), (9w₂₅₆,−w₂₅₆),

(7w₂₅₆,15w₂₅₆), (7w₂₅₆,13w₂₅₆), (7w₂₅₆,11w₂₅₆), (7w₂₅₆,9w₂₅₆),(7w₂₅₆,7w₂₅₆), (7w₂₅₆,5w₂₅₆), (7w₂₅₆,3w₂₅₆), (7w₂₅₆,w₂₅₆),

(7w₂₅₆,−15w₂₅₆), (7w₂₅₆,−13w₂₅₆), (7w₂₅₆,−11w₂₅₆), (7w₂₅₆,−9w₂₅₆),(7w₂₅₆,−7w₂₅₆), (7w₂₅₆,−5w₂₅₆), (7w₂₅₆,−3w₂₅₆), (7w₂₅₆,−w₂₅₆),

(5w₂₅₆,15w₂₅₆), (5w₂₅₆,13w₂₅₆), (5w₂₅₆,11w₂₅₆), (5w₂₅₆,9w₂₅₆),(5w₂₅₆,7w₂₅₆), (5w₂₅₆,5w₂₅₆), (5w₂₅₆,3w₂₅₆), (5w₂₅₆,w₂₅₆),

(5w₂₅₆,−15w₂₅₆), (5w₂₅₆,−13w₂₅₆), (5w₂₅₆,−11w₂₅₆), (5w₂₅₆,−9w₂₅₆),(5w₂₅₆,−7w₂₅₆), (5w₂₅₆,−5w₂₅₆), (5w₂₅₆,−3w₂₅₆), (5w₂₅₆,−w₂₅₆),

(3w₂₅₆,15w₂₅₆), (3w₂₅₆,13w₂₅₆), (3w₂₅₆,11w₂₅₆), (3w₂₅₆,9w₂₅₆),(3w₂₅₆,7w₂₅₆), (3w₂₅₆,5w₂₅₆), (3w₂₅₆,3w₂₅₆), (3w₂₅₆,w₂₅₆),

(3w₂₅₆,−15w₂₅₆), (3w₂₅₆,−13w₂₅₆), (3w₂₅₆,−11w₂₅₆), (3w₂₅₆,−9w₂₅₆),(3w₂₅₆,−7w₂₅₆), (3w₂₅₆,−5w₂₅₆), (3w₂₅₆,−3w₂₅₆), (3w₂₅₆,−w₂₅₆),

(w₂₅₆,15w₂₅₆), (w₂₅₆,13w₂₅₆), (w₂₅₆,11w₂₅₆), (w₂₅₆,9w₂₅₆), (w₂₅₆,7w₂₅₆),(w₂₅₆,5w₂₅₆), (w₂₅₆,3w₂₅₆), (w₂₅₆,w₂₅₆),

(w₂₅₆,−15w₂₅₆), (w₂₅₆,−13w₂₅₆), (w₂₅₆,−11w₂₅₆), (w₂₅₆,−9w₂₅₆),(w₂₅₆,−7w₂₅₆), (w₂₅₆,−5w₂₅₆), (w₂₅₆,−3w₂₅₆), (w₂₅₆,−w₂₅₆),

(−15w₂₅₆,15w₂₅₆), (−15w₂₅₆,13w₂₅₆), (−15w₂₅₆,11w₂₅₆), (−15w₂₅₆,9w₂₅₆),(−15w₂₅₆,7w₂₅₆), (−15w₂₅₆,5w₂₅₆), (−15w₂₅₆,3w₂₅₆), (−15w₂₅₆,w₂₅₆),

(−15w₂₅₆,−15w₂₅₆), (−15w₂₅₆,−13w₂₅₆), (−15w₂₅₆,−11w₂₅₆),(−15w₂₅₆,−9w₂₅₆), (−15w₂₅₆,−7w₂₅₆), (−15w₂₅₆,−5w₂₅₆), (−15w₂₅₆,−3w₂₅₆),(−15w₂₅₆,−w₂₅₆),

(−13w₂₅₆,15w₂₅₆), (−13w₂₅₆,13w₂₅₆), (−13w₂₅₆,11w₂₅₆), (−13w₂₅₆,9w₂₅₆),(−13w₂₅₆,7w₂₅₆), (−13w₂₅₆,5w₂₅₆), (−13w₂₅₆,3w₂₅₆), (−13w₂₅₆,w₂₅₆),

(−13w₂₅₆,−15w₂₅₆), (−13w₂₅₆,−13w₂₅₆), (−13w₂₅₆,−11w₂₅₆),(−13w₂₅₆,−9w₂₅₆), (−13w₂₅₆,−7w₂₅₆), (−13w₂₅₆,−5w₂₅₆), (−13w₂₅₆,−3w₂₅₆),(−13w₂₅₆,−w₂₅₆),

(−11w₂₅₆,15w₂₅₆), (−11w₂₅₆,13w₂₅₆), (−11w₂₅₆,11w₂₅₆), (−11w₂₅₆,9w₂₅₆),(−11w₂₅₆,7w₂₅₆), (−11w₂₅₆,5w₂₅₆), (−11w₂₅₆,3w₂₅₆), (−11w₂₅₆,w₂₅₆),

(−11w₂₅₆,−15w₂₅₆), (−11w₂₅₆,−13w₂₅₆), (−11w₂₅₆,−11w₂₅₆),(−11w₂₅₆,−9w₂₅₆), (−11w₂₅₆,−7w₂₅₆), (−11w₂₅₆,−5w₂₅₆), (−11w₂₅₆,−3w₂₅₆),(−11w₂₅₆,−w₂₅₆),

(−9w₂₅₆,15w₂₅₆), (−9w₂₅₆,13w₂₅₆), (−9w₂₅₆,11w₂₅₆), (−9w₂₅₆,9w₂₅₆),(−9w₂₅₆,7w₂₅₆), (−9w₂₅₆,5w₂₅₆), (−9w₂₅₆,3w₂₅₆), (−9w₂₅₆,w₂₅₆),

(−9w₂₅₆,−15w₂₅₆), (−9w₂₅₆,−13w₂₅₆), (−9w₂₅₆,−11w₂₅₆), (−9w₂₅₆,−9w₂₅₆),(−9w₂₅₆,−7w₂₅₆), (−9w₂₅₆,−5w₂₅₆), (−9w₂₅₆,−3w₂₅₆), (−9w₂₅₆,−w₂₅₆),

(−7w₂₅₆,15w₂₅₆), (−7w₂₅₆,13w₂₅₆), (−7w₂₅₆,11w₂₅₆), (−7w₂₅₆,9w₂₅₆),(−7w₂₅₆,7w₂₅₆), (−7w₂₅₆,5w₂₅₆), (−7w₂₅₆,3w₂₅₆), (−7w₂₅₆,w₂₅₆),

(−7w₂₅₆,−15w₂₅₆), (−7w₂₅₆,−13w₂₅₆), (−7w₂₅₆,−11w₂₅₆), (−7w₂₅₆,−9w₂₅₆),(−7w₂₅₆,−7w₂₅₆), (−7w₂₅₆,−5w₂₅₆), (−7w₂₅₆,−3w₂₅₆), (−7w₂₅₆,−w₂₅₆),

(−5w₂₅₆,15w₂₅₆), (−5w₂₅₆,13w₂₅₆), (−5w₂₅₆,11w₂₅₆), (−5w₂₅₆,9w₂₅₆),(−5w₂₅₆,7w₂₅₆), (−5w₂₅₆,5w₂₅₆), (−5w₂₅₆,3w₂₅₆), (−5w₂₅₆,w₂₅₆),

(−5w₂₅₆,−15w₂₅₆), (−5w₂₅₆,−13w₂₅₆), (−5w₂₅₆,−11w₂₅₆), (−5w₂₅₆,−9w₂₅₆),(−5w₂₅₆,−7w₂₅₆), (−5w₂₅₆,−5w₂₅₆), (−5w₂₅₆,−3w₂₅₆), (−5w₂₅₆,−w₂₅₆),

(−3w₂₅₆,15w₂₅₆), (−3w₂₅₆,13w₂₅₆), (−3w₂₅₆,11w₂₅₆), (−3w₂₅₆,9w₂₅₆),(−3w₂₅₆,7w₂₅₆), (−3w₂₅₆,5w₂₅₆), (−3w₂₅₆,3w₂₅₆), (−3w₂₅₆,w₂₅₆),

(−3w₂₅₆,−15w₂₅₆), (−3w₂₅₆,−13w₂₅₆), (−3w₂₅₆,−11w₂₅₆), (−3w₂₅₆,−9w₂₅₆),(−3w₂₅₆,−7w₂₅₆), (−3w₂₅₆,−5w₂₅₆), (−3w₂₅₆,−3w₂₅₆), (−3w₂₅₆,−w₂₅₆),

(−w₂₅₆,15w₂₅₆), (−w₂₅₆,13w₂₅₆), (−w₂₅₆,11w₂₅₆), (−w₂₅₆,9w₂₅₆),(−w₂₅₆,7w₂₅₆), (−w₂₅₆,5w₂₅₆), (−w₂₅₆,3w₂₅₆), (−w₂₅₆,w₂₅₆),

(−w₂₅₆,−15w₂₅₆), (−w₂₅₆,−w₂₅₆), (−w₂₅₆,−11w₂₅₆), (−w₂₅₆,−9w₂₅₆),(−w₂₅₆,−7w₂₅₆), (−w₂₅₆,−5w₂₅₆), (−w₂₅₆,−3w₂₅₆), (−w₂₅₆,−w₂₅₆)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, b5, b6, and b7. For example, in the case that the bitsto be transmitted is (b0, b1, b2, b3, b4, b5, b6, b7)=(0,0,0,0,0,0,0,0),the bits are mapped at signal point 2001 in FIG. 20 , and(I,Q)=(15w₂₅₆,15w₂₅₆) is obtained when I is an in-phase component whileQ is a quadrature component of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5, b6, b7),in-phase component I and quadrature component Q of the mapped basebandsignal are decided (during 256QAM modulation). FIG. 20 illustrates anexample of a relationship between the set of b0, b1, b2, b3, b4, b5, b6,and b7 (00000000 to 11111111) and the signal point coordinates. Values00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6, and b7are indicated immediately below 256 signal points included in 256QAM(the marks “◯” in FIG. 20 ) (15w₂₅₆,15w₂₅₆), (15w₂₅₆,13w₂₅₆),(15w₂₅₆,11w₂₅₆), (15w₂₅₆,9w₂₅₆), (15w₂₅₆,7w₂₅₆), (15w₂₅₆,5w₂₅₆),(15w₂₅₆,3w₂₅₆), (15w₂₅₆,w₂₅₆),

(15w₂₅₆,−15w₂₅₆), (15w₂₅₆,−13w₂₅₆), (15w₂₅₆,−11w₂₅₆), (15w₂₅₆,−9w₂₅₆),(15w₂₅₆,−7w₂₅₆), (15w₂₅₆,−5w₂₅₆), (15w₂₅₆,−3w₂₅₆), (15w₂₅₆,−w₂₅₆),

(13w₂₅₆,15w₂₅₆), (13w₂₅₆,13w₂₅₆), (13w₂₅₆,11w₂₅₆), (13w₂₅₆,9w₂₅₆),(13w₂₅₆,7w₂₅₆), (13w₂₅₆,5w₂₅₆), (13w₂₅₆,3w₂₅₆), (13w₂₅₆,w₂₅₆),

(13w₂₅₆,−15w₂₅₆), (13w₂₅₆,−13w₂₅₆), (13w₂₅₆,−11w₂₅₆), (13w₂₅₆,−9w₂₅₆),(13w₂₅₆,−7w₂₅₆), (13w₂₅₆,−5w₂₅₆), (13w₂₅₆,−3w₂₅₆), (13w₂₅₆,−w₂₅₆),

(11w₂₅₆,15w₂₅₆), (11w₂₅₆,13w₂₅₆), (11w₂₅₆,11w₂₅₆), (11w₂₅₆,9w₂₅₆),(11w₂₅₆,7w₂₅₆), (11w₂₅₆,5w₂₅₆), (11w₂₅₆,3w₂₅₆), (11w₂₅₆,w₂₅₆),

(11w₂₅₆,−15w₂₅₆), (11w₂₅₆,−13w₂₅₆), (11w₂₅₆,−11w₂₅₆), (11w₂₅₆,−9w₂₅₆),(11w₂₅₆,−7w₂₅₆), (11w₂₅₆,−5w₂₅₆), (11w₂₅₆,−3w₂₅₆), (11w₂₅₆,−w₂₅₆),

(9w₂₅₆,15w₂₅₆), (9w₂₅₆,13w₂₅₆), (9w₂₅₆,11w₂₅₆), (9w₂₅₆,9w₂₅₆),(9w₂₅₆,7w₂₅₆), (9w₂₅₆,5w₂₅₆), (9w₂₅₆,3w₂₅₆), (9w₂₅₆,w₂₅₆),

(9w₂₅₆,−15w₂₅₆), (9w₂₅₆,−13w₂₅₆), (9w₂₅₆,−11w₂₅₆), (9w₂₅₆,−9w₂₅₆),(9w₂₅₆,−7w₂₅₆), (9w₂₅₆,−5w₂₅₆), (9w₂₅₆,−3w₂₅₆), (9w₂₅₆,−w₂₅₆),

(7w₂₅₆,15w₂₅₆), (7w₂₅₆,13w₂₅₆), (7w₂₅₆,11w₂₅₆), (7w₂₅₆,9w₂₅₆),(7w₂₅₆,7w₂₅₆), (7w₂₅₆,5w₂₅₆), (7w₂₅₆,3w₂₅₆), (7w₂₅₆,w₂₅₆),

(7w₂₅₆,−15w₂₅₆), (7w₂₅₆,−13w₂₅₆), (7w₂₅₆,−11w₂₅₆), (7w₂₅₆,−9w₂₅₆),(7w₂₅₆,−7w₂₅₆), (7w₂₅₆,−5w₂₅₆), (7w₂₅₆,−3w₂₅₆), (7w₂₅₆,−w₂₅₆),

(5w₂₅₆,15w₂₅₆), (5w₂₅₆,13w₂₅₆), (5w₂₅₆,11w₂₅₆), (5w₂₅₆,9w₂₅₆),(5w₂₅₆,7w₂₅₆), (5w₂₅₆,5w₂₅₆), (5w₂₅₆,3w₂₅₆), (5w₂₅₆,w₂₅₆),

(5w₂₅₆,−15w₂₅₆), (5w₂₅₆,−13w₂₅₆), (5w₂₅₆,−11w₂₅₆), (5w₂₅₆,−9w₂₅₆),(5w₂₅₆,−7w₂₅₆), (5w₂₅₆,−5w₂₅₆), (5w₂₅₆,−3w₂₅₆), (5w₂₅₆,−w₂₅₆),

(3w₂₅₆,15w₂₅₆), (3w₂₅₆,13w₂₅₆), (3w₂₅₆,11w₂₅₆), (3w₂₅₆,9w₂₅₆),(3w₂₅₆,7w₂₅₆), (3w₂₅₆,5w₂₅₆), (3w₂₅₆,3w₂₅₆), (3w₂₅₆,w₂₅₆),

(3w₂₅₆,−15w₂₅₆), (3w₂₅₆,−13w₂₅₆), (3w₂₅₆,−11w₂₅₆), (3w₂₅₆,−9w₂₅₆),(3w₂₅₆,−7w₂₅₆), (3w₂₅₆,−5w₂₅₆), (3w₂₅₆,−3w₂₅₆), (3w₂₅₆,−w₂₅₆),

(w₂₅₆,15w₂₅₆), (w₂₅₆,13w₂₅₆), (w₂₅₆,11w₂₅₆), (w₂₅₆,9w₂₅₆), (w₂₅₆,7w₂₅₆),(w₂₅₆,5w₂₅₆), (w₂₅₆,3w₂₅₆), (w₂₅₆,w₂₅₆),

(w₂₅₆,−15w₂₅₆), (w₂₅₆,−13w₂₅₆), (w₂₅₆,−11w₂₅₆), (w₂₅₆,−9w₂₅₆),(w₂₅₆,−7w₂₅₆), (w₂₅₆,−5w₂₅₆), (w₂₅₆,−3w₂₅₆), (w₂₅₆,−w₂₅₆),

(−15w₂₅₆,15w₂₅₆), (−15w₂₅₆,13w₂₅₆), (−15w₂₅₆,11w₂₅₆), (−15w₂₅₆,9w₂₅₆),(−15w₂₅₆,7w₂₅₆), (−15w₂₅₆,5w₂₅₆), (−15w₂₅₆,3w₂₅₆), (−15w₂₅₆,w₂₅₆),

(−15w₂₅₆,−15w₂₅₆), (−15w₂₅₆,−13w₂₅₆), (−15w₂₅₆,−11w₂₅₆),(−15w₂₅₆,−9w₂₅₆), (−15w₂₅₆,−7w₂₅₆), (−15w₂₅₆,−5w₂₅₆), (−15w₂₅₆,−3w₂₅₆),(−15w₂₅₆,−w₂₅₆),

(−13w₂₅₆,15w₂₅₆), (−13w₂₅₆,13w₂₅₆), (−13w₂₅₆,11w₂₅₆), (−13w₂₅₆,9w₂₅₆),(−13w₂₅₆,7w₂₅₆), (−13w₂₅₆,5w₂₅₆), (−13w₂₅₆,3w₂₅₆), (−13w₂₅₆,w₂₅₆),

(−13w₂₅₆,−15w₂₅₆), (−13w₂₅₆,−13w₂₅₆), (−13w₂₅₆,−11w₂₅₆),(−13w₂₅₆,−9w₂₅₆), (−13w₂₅₆,−7w₂₅₆), (−13w₂₅₆,−5w₂₅₆), (−13w₂₅₆,−3w₂₅₆),(−13w₂₅₆,−w₂₅₆),

(−11w₂₅₆,15w₂₅₆), (−11w₂₅₆,13w₂₅₆), (−11w₂₅₆,11w₂₅₆), (−11w₂₅₆,9w₂₅₆),(−11w₂₅₆,7w₂₅₆), (−11w₂₅₆,5w₂₅₆), (−11w₂₅₆,3w₂₅₆), (−11w₂₅₆,w₂₅₆),

(−11w₂₅₆,−15w₂₅₆), (−11w₂₅₆,−13w₂₅₆), (−11w₂₅₆,−11w₂₅₆),(−11w₂₅₆,−9w₂₅₆), (−11w₂₅₆,−7w₂₅₆), (−11w₂₅₆,−5w₂₅₆), (−11w₂₅₆,−3w₂₅₆),(−11w₂₅₆,−w₂₅₆),

(−9w₂₅₆,15w₂₅₆), (−9w₂₅₆,13w₂₅₆), (−9w₂₅₆,11w₂₅₆), (−9w₂₅₆,9w₂₅₆),(−9w₂₅₆,7w₂₅₆), (−9w₂₅₆,5w₂₅₆), (−9w₂₅₆,3w₂₅₆), (−9w₂₅₆,w₂₅₆),

(−9w₂₅₆,−15w₂₅₆), (−9w₂₅₆,−13w₂₅₆), (−9w₂₅₆,−11w₂₅₆), (−9w₂₅₆,−9w₂₅₆),(−9w₂₅₆,−7w₂₅₆), (−9w₂₅₆,−5w₂₅₆), (−9w₂₅₆,−3w₂₅₆), (−9w₂₅₆,−w₂₅₆),

(−7w₂₅₆,15w₂₅₆), (−7w₂₅₆,13w₂₅₆), (−7w₂₅₆,11w₂₅₆), (−7w₂₅₆,9w₂₅₆),(−7w₂₅₆,7w₂₅₆), (−7w₂₅₆,5w₂₅₆), (−7w₂₅₆,3w₂₅₆), (−7w₂₅₆,w₂₅₆),

(−7w₂₅₆,−15w₂₅₆), (−7w₂₅₆,−13w₂₅₆), (−7w₂₅₆,−11w₂₅₆), (−7w₂₅₆,−9w₂₅₆),(−7w₂₅₆,−7w₂₅₆), (−7w₂₅₆,−5w₂₅₆), (−7w₂₅₆,−3w₂₅₆), (−7w₂₅₆,−w₂₅₆),

(−5w₂₅₆,15w₂₅₆), (−5w₂₅₆,13w₂₅₆), (−5w₂₅₆,11w₂₅₆), (−5w₂₅₆,9w₂₅₆),(−5w₂₅₆,7w₂₅₆), (−5w₂₅₆,5w₂₅₆), (−5w₂₅₆,3w₂₅₆), (−5w₂₅₆,w₂₅₆),

(−5w₂₅₆,−15w₂₅₆), (−5w₂₅₆,−13w₂₅₆), (−5w₂₅₆,−11w₂₅₆), (−5w₂₅₆,−9w₂₅₆),(−5w₂₅₆,−7w₂₅₆), (−5w₂₅₆,−5w₂₅₆), (−5w₂₅₆,−3w₂₅₆), (−5w₂₅₆,−w₂₅₆),

(−3w₂₅₆,15w₂₅₆), (−3w₂₅₆,13w₂₅₆), (−3w₂₅₆,11w₂₅₆), (−3w₂₅₆,9w₂₅₆),(−3w₂₅₆,7w₂₅₆), (−3w₂₅₆,5w₂₅₆), (−3w₂₅₆,3w₂₅₆), (−3w₂₅₆,w₂₅₆),

(−3w₂₅₆,−15w₂₅₆), (−3w₂₅₆,−13w₂₅₆), (−3w₂₅₆,−11w₂₅₆), (−3w₂₅₆,−9w₂₅₆),(−3w₂₅₆,−7w₂₅₆), (−3w₂₅₆,−5w₂₅₆), (−3w₂₅₆,−3w₂₅₆), (−3w₂₅₆,−w₂₅₆),

(−w₂₅₆,15w₂₅₆), (−w₂₅₆,13w₂₅₆), (−w₂₅₆,11w₂₅₆), (−w₂₅₆,9w₂₅₆),(−w₂₅₆,7w₂₅₆), (−w₂₅₆,5w₂₅₆), (−w₂₅₆,3w₂₅₆), (−w₂₅₆,w₂₅₆),

(−w₂₅₆,−15w₂₅₆), (−w₂₅₆,−w₂₅₆), (−w₂₅₆,−11w₂₅₆), (−w₂₅₆,−9w₂₅₆),(−w₂₅₆,−7w₂₅₆), (−w₂₅₆,−5w₂₅₆), (−w₂₅₆,−3w₂₅₆), (−w₂₅₆,−w₂₅₆).Respective coordinates of the signal points (“◯”) immediately above thevalues 00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6,and b7 in the I-Q plane serve as in-phase component I and quadraturecomponent Q of the mapped baseband signal.The relationship between the set of b0, b1, b2, b3, b4, b5, b6, and b7(00000000 to 11111111) and the signal point coordinates during 256QAMmodulation is not limited to that in FIG. 20 . A complex value ofin-phase component I and quadrature component Q of the mapped basebandsignal (during 256QAM modulation) serves as a baseband signal (s₁(t) ors₂(t) in FIGS. 5 to 7 ).

In this case, the modulation scheme of baseband signal 505A (s₁(t)(s₁(i))) is set to 256QAM while modulation scheme of baseband signal505B (s₂(t) (s₂(i))) is set to 64QAM in FIG. 5 to FIG. 7 . Theconfiguration of the precoding matrix will be described below.

At this point, generally average power of baseband signal 505A (s₁(t)and (s₁(i))) and average power of baseband signal 505B (s₂(t) and(s₂(i))), which are of the output of mapper 504 in FIGS. 5 to 7 , areequalized to each other. Accordingly, the following relationalexpression holds with respect to coefficient w₆₄ of the 64QAM mappingmethod and coefficient w₂₅₆ of the 256QAM mapping method.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 263} \right\rbrack & \; \\{w_{64} = \frac{z}{\sqrt{42}}} & {{Formula}\mspace{14mu}({S224})} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 264} \right\rbrack & \; \\{w_{256} = \frac{z}{\sqrt{170}}} & {{Formula}\mspace{14mu}({S225})}\end{matrix}$

In equations (S224) and (S225), it is assumed that z is a real numberlarger than 0. When the calculations are performed in <1> to <5>,

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

the configuration of precoding matrix F

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 265} \right\rbrack & \; \\{F = \begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}} & {\mspace{14mu}({S226})}\end{matrix}$

will be described in detail below ((Example 4-1) to (Example 4-8)).

Example 4-1

For one of <1> to <5>, precoding matrix F is set to one of the followingequations.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 266} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S227})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 267} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S228})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 268} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S229})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 269} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S230})}\end{matrix}$

In equations (S227), (S228), (S229), and (S230), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 270} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}}} & {{Formula}\mspace{14mu}({S231})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 271} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}}} & {{Formula}\mspace{14mu}({S232})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 272} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8} \times e^{j\frac{\pi}{2}}}} & {{Formula}\mspace{14mu}({S233})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 273} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8} \times e^{j\frac{3\;\pi}{2}}}} & {{Formula}\mspace{14mu}({S234})}\end{matrix}$

The modulation scheme of baseband signal 505A (s₁(t) (s₁(i))) is set to256QAM while modulation scheme of baseband signal 505B (s₂(t) (s₂(i)))is set to 64QAM. Accordingly, the precoding (and the phase change andthe power change) is performed to transmit the modulated signal fromeach antenna as described above, the total number of bits transmittedusing symbols transmitted from antenna 808A and 808B in FIG. 8 at the(unit) time of time u and frequency (carrier) v is 14 bits that are of asum of 6 bits (for the use of 64QAM) and 8 bits (for the use of 256QAM).

Assuming that b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) andb_(5,64) are input bits for the purpose of the 64QAM mapping, and thatb_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), and b_(7,256) are input bits for the purpose of the 256QAMmapping, even if value α in any one of equations (S231), (S232), (S233),and (S234) is used,

in signal z₁(t) (z₁(i)),

the signal point at which (b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64) b_(5,64), b_(0,256), b_(1,256), b_(2,256), b_(3,256),b_(4,256), b_(5,256), b_(6,256), b_(7,256)) corresponds to(0,0,0,0,0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64), b_(0,256), b_(1,256),b_(2,256), b_(3,256), b_(4,256), b_(5,256), b_(6,256), b_(7,256))corresponds to (1,1,1,1,1,1,1,1,1,1,1,1,1,1) exist in the I-Q plane,similarly, in signal z₂(t) (z₂(i)),the signal point at which (b_(0,64), b_(1,64), b_(2,64), b_(3,64),b_(4,64) b_(5,64), b_(0,256), b_(1,256), b_(2,256), b_(3,256),b_(4,256), b_(5,256), b_(6,256), b_(7,256)) corresponds to(0,0,0,0,0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64), b_(0,256), b_(1,256),b_(2,256), b_(3,256), b_(4,256), b_(5,256), b_(6,256), b_(7,256))corresponds to (1,1,1,1,1,1,1,1,1,1,1,1,1,1) exist in the I-Q plane.

In the above description, with respect to signal z₂(t) (z₂(i)) inequations (s2), (S3), (S4), (S5), and (S8), equations (S231) to (S243)are considered as value α with which the receiver obtains the good datareception quality. This point will be described below. In signal z₂(t)(z₂(i)), the signal point at which (b_(0,64), b_(1,64), b_(2,64),b_(3,64), b_(4,64) b_(5,64), b_(0,256), b_(1,256), b_(2,256), b_(3,256),b_(4,256), b_(5,256), b_(6,256), b_(7,256)) corresponds to(0,0,0,0,0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64), b_(0,256), b_(1,256),b_(2,256), b_(3,256), b_(4,256), b_(5,256), b_(6,256), b_(7,256))corresponds to (1,1,1,1,1,1,1,1,1,1,1,1,1,1) exists in the I-Q plane,and it is desirable that 2¹⁴=16384 signal points exist in the I-Q planewhile not overlapping one another.

This is attributed to the following fact. That is, the receiver performsthe detection and the error correction decoding using signal z₂(t)(z₂(i)) in the case that a modulated signal transmitted from the antennafor transmitting signal z₁(t) (z₁(i)) does not reach the receiver, andit is necessary at that time that the 16384 signal points exist in theI-Q plane while not overlapping one another in order that the receiverobtains the high data reception quality.

In the case that precoding matrix F is set to one of equations (S227),(S228), (S229), and (S230), and that α is set to one of equations(S231), (S232), (S233), and (S234), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, the arrangement of the signal points existing in afirst quadrant is obtained as illustrated in FIG. 37 , the arrangementof the signal points existing in a second quadrant is obtained asillustrated in FIG. 38 , the arrangement of the signal points existingin a third quadrant is obtained as illustrated in FIG. 39 , and thearrangement of the signal points existing in a fourth quadrant isobtained as illustrated in FIG. 40 . In FIGS. 37, 38, 39, and 40 , ahorizontal axis indicates I, and a vertical axis indicates Q, a mark “●”indicates a signal point, and a mark “Δ” indicates origin (0).

As can be seen from FIGS. 37, 38, 39, and 40 , the 16384 signal pointsexist while not overlapping one another in the I-Q plane. On the I-Qplane, Euclidean distances between closest signal points are equal inthe 16380 signal points of the 16384 signal points except for therightmost and uppermost point in FIG. 37 , the rightmost and lowermostpoint in FIG. 40 , the leftmost and uppermost point in FIG. 38 , and theleftmost and lowermost point in FIG. 39 . Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S227),(S228), (S229), and (S230), and that α is set to one of equations(S231), (S232), (S233), and (S234), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, the arrangement of the signal points existing inthe first quadrant is obtained as illustrated in FIG. 41 , thearrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 42 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.43 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 44 . In FIGS. 41, 42, 43,and 44 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 41, 42, 43, and 44 , the 16384 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 16384signal points in FIGS. 37, 38, 39, and 40 , and that D₁ is a minimumEuclidean distance at the 16384 signal points in FIGS. 41, 42, 43, and44 . D₁<D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁<Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 4-2

Then, equations (S224) and (S225) hold with respect to coefficient w₆₄of the 64QAM mapping method and coefficient w₂₅₆ of the 256QAM mappingmethod, and precoding matrix F is set to one of equations (S235),(S236), (S237), and (S238) when the calculations are performed in <1> to<5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 274} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S235})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 275} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S236})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 276} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S237})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 277} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S238})}\end{matrix}$

In equations (S235) and (S237), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 278} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}} \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S239})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 279} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{9}{8}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S240})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 280} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}} \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S241})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 281} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{9}{8}} \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S242})}\end{matrix}$

In equations (S239), (S240), (S241), and (S242), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 282} \right\rbrack & \; \\{{{- \frac{\pi}{2}}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}({radian})}} & {{Formula}\mspace{14mu}({S243})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S235),(S236), (S237), and (S238), and that θ is set to one of equations(S239), (S240), (S241), and (S242), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 37 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 38 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.39 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 40 . In FIGS. 37, 38, 39,and 2540 , a horizontal axis indicates I, and a vertical axis indicatesQ, a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 37, 38, 39, and 40 , the 16384 signal pointsexist while not overlapping one another in the I-Q plane. On the I-Qplane, Euclidean distances between closest signal points are equal inthe 16380 signal points of the 16384 signal points except for therightmost and uppermost point in FIG. 37 , the rightmost and lowermostpoint in FIG. 40 , the leftmost and uppermost point in FIG. 38 , and theleftmost and lowermost point in FIG. 39 . Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S235),(S236), (S237), and (S238), and that θ is set to one of equations(S239), (S240), (S241), and (S242), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 41 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 42 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.43 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 44 . In FIGS. 41,42, 43, and44 , a horizontal axis indicates I, and a vertical axis indicates Q, amark “●” indicates a signal point, and a mark “Δ” indicates origin (0).

As can be seen from FIGS. 41, 42, 43, and 44 , the 16384 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 16384signal points in FIGS. 37, 38, 39, and 40 , and that D₁ is a minimumEuclidean distance at the 16384 signal points in FIGS. 41, 42, 43, and44 . D₁<D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁<Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 4-3

Equations (S224) and (S225) hold with respect to coefficient w₆₄ of the64QAM mapping method and coefficient w₂₅₆ of the 256QAM mapping method,and precoding matrix F is set to one of equations (S173), (S174),(S175), and (S176) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (S2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 283} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S244})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 284} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S245})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 285} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S246})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 286} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S247})}\end{matrix}$

In equations (S244), (S245), (S246), and (S247), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 287} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9}}} & {{Formula}\mspace{14mu}({S248})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 288} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{8}{9}}} & {{Formula}\mspace{14mu}({S249})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 289} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9} \times e^{j\frac{\pi}{2}}}} & {{Formula}\mspace{14mu}({S250})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 290} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9} \times e^{j\frac{3\;\pi}{2}}}} & {{Formula}\mspace{14mu}({S251})}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S244),(S245), (S246), and (S247), and that α is set to one of equations(S248), (S249), (S250), and (S251), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 45 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 46 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.47 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 48 . In FIGS. 45, 46, 47,and 48 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 45, 46, 47, and 48 , the 16384 signal pointsexist while not overlapping one another in the I-Q plane. On the I-Qplane, Euclidean distances between closest signal points are equal inthe 16380 signal points of the 16384 signal points except for therightmost and uppermost point in FIG. 45 , the rightmost and lowermostpoint in FIG. 48 , the leftmost and uppermost point in FIG. 46 , and theleftmost and lowermost point in FIG. 47 . Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S244),(S245), (S246), and (S247), and that α is set to one of equations(S248), (S249), (S250), and (S251), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 49 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 50 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.51 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 52 . In FIGS. 49, 50, 51,and 52 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 49, 50, 51, and 52 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 16384signal points in FIGS. 45, 46, 47, and 48 , and that D₁ is a minimumEuclidean distance at the 16384 signal points in FIGS. 49, 50, 51, and52 . D₁<D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁<Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 4-4

Then, equations (S224) and (S225) hold with respect to coefficient w₆₄of the 64QAM mapping method and coefficient w₂₅₆ of the 256QAM mappingmethod, and precoding matrix F is set to one of equations (S235),(S236), (S237), and (S238) when the calculations are performed in <1> to<5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 291} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {\beta \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {{- \beta} \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S252})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 292} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {\sin\;\theta} \\{\sin\;\theta} & {{- \cos}\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S253})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 293} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times \cos\;\theta} & {{- \beta} \times \sin\;\theta} \\{\beta \times \sin\;\theta} & {\beta \times \cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S254})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 294} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\;\theta} & {{- \sin}\;\theta} \\{\sin\;\theta} & {\cos\;\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}({S255})}\end{matrix}$

In equations (S252) and (S254), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 295} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9}}\; \right)}\mspace{11mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9}}\; \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S256})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 296} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9}}\; \right)}\mspace{11mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{170}}{\sqrt{42}} \times \frac{8}{9}}\; \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S257})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 297} \right\rbrack & \; \\{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{8}{9}}\; \right)}\mspace{11mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{8}{9}}\; \right)}} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S258})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 298} \right\rbrack & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{8}{9}}\; \right)}\mspace{11mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{170}}{\sqrt{42}}} \times \frac{8}{9}}\; \right)} + {2n\;{\pi({radian})}}}} & {{Formula}\mspace{14mu}({S259})}\end{matrix}$

In equations (S256), (S257), (S258), and (S259), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 299} \right\rbrack & \; \\{{{- \frac{\pi}{2}}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}({radian})}} & {{Formula}\mspace{14mu}({S260})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S252),(S253), (S254), and (S255), and that θ is set to one of equations(S256), (S257), (S258), and (S259), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 45 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 46 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.47 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 48 . In FIGS. 45, 46, 47,and 48 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 45, 46, 47, and 48 , the 16384 signal pointsexist while not overlapping one another in the I-Q plane. On the I-Qplane, Euclidean distances between closest signal points are equal inthe 16380 signal points of the 16384 signal points except for therightmost and uppermost point in FIG. 45 , the rightmost and lowermostpoint in FIG. 48 , the leftmost and uppermost point in FIG. 46 , and theleftmost and lowermost point in FIG. 47 . Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S252),(S253), (S254), and (S255), and that θ is set to one of equations(S256), (S257), (S258), and (S259), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 49 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 50 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.51 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 52 . In FIGS. 49, 50, 51,and 52 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 49, 50, 51, and 52 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 16384signal points in FIGS. 45, 46, 47, and 48 , and that D₁ is a minimumEuclidean distance at the 16384 signal points in FIGS. 49, 50, 51, and52 . D₁<D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁<Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 4-5

Equations (S224) and (S225) hold with respect to coefficient w₆₄ of the64QAM mapping method and coefficient w₂₅₆ of the 256QAM mapping method,and precoding matrix F is set to one of equations (S173), (S174),(S175), and (S176) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 300} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}} & {{Formula}\mspace{14mu}({S261})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 301} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S262})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 302} \right\rbrack & \; \\{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}} & {{Formula}\mspace{14mu}\left( {S263} \right.} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 303} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}}} & {{Formula}\mspace{14mu}({S264})}\end{matrix}$

In equations (S261), (S262), (S263), and (S264), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, a is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 304} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8}}} & {{Formula}\mspace{14mu}({S265})} \\{or} & \; \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 305} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}}} & {{Formula}\mspace{14mu}({S266})}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 306} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8} \times e^{j\frac{\pi}{2}}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 267} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 307} \right\rbrack & \; \\{\alpha = {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}\left( {S\; 268} \right)}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S261),(S262), (S263), and (S264), and that α is set to one of equations(S265), (S266), (S267), and (S268), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 21 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 22 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.23 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 24 . In FIGS. 21,22, 23, and24 , a horizontal axis indicates I, and a vertical axis indicates Q, amark “●” indicates a signal point, and a mark “Δ” indicates origin (0).

As can be seen from FIGS. 21, 22, 23, and 24 , the 16384 signal pointsexist while not overlapping one another. On the I-Q plane, Euclideandistances between closest signal points are equal in the 16380 signalpoints of the 16384 signal points except for the rightmost and uppermostpoint in FIG. 21 , the rightmost and lowermost point in FIG. 24 , theleftmost and uppermost point in FIG. 22 , and the leftmost and lowermostpoint in FIG. 23 . Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S261),(S262), (S263), and (S264), and that α is set to one of equations(S265), (S266), (S267), and (S268), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 25 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 26 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.27 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 28 . In FIGS. 25, 26, 27,and 28 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 25, 26, 27, and 28 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 16384signal points in FIGS. 21, 22, 23, and 24 , and that D₂ is a minimumEuclidean distance at the 16384 signal points in FIGS. 25, 26, 27, and28 . D₁>D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁>Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 4-6

Then, equations (S224) and (S225) hold with respect to coefficient w₆₄of the 64QAM mapping method and coefficient w₂₅₆ of the 256QAM mappingmethod, and precoding matrix F is set to one of equations (S235),(S236), (S237), and (S238) when the calculations are performed in <1> to<5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 308} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{14mu}\theta} & {\beta \times \sin\mspace{14mu}\theta} \\{\beta \times \sin\mspace{14mu}\theta} & {{- \beta} \times \cos\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 269} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 309} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\mspace{14mu}\theta} & {\sin\mspace{14mu}\theta} \\{\sin\mspace{14mu}\theta} & {{- \cos}\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 270} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 310} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{14mu}\theta} & {{- \beta} \times \sin\mspace{14mu}\theta} \\{\beta \times \sin\mspace{14mu}\theta} & {\beta \times \cos\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 271} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 311} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\mspace{14mu}\theta} & {{- \sin}\mspace{14mu}\theta} \\{\sin\mspace{14mu}\theta} & {\cos\mspace{14mu}\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}\left( {S\; 272} \right)}\end{matrix}$

In equations (S269) and (S271), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 312} \right\rbrack} & \; \\{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8}} \right)}} + {2n\;\pi\mspace{14mu}({radian})\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}\left( {S\; 273} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 313} \right\rbrack} & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{9}{8}} \right)} + {2n\;\pi\mspace{14mu}({radian})\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}\left( {S\; 274} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 314} \right\rbrack} & \; \\{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}} \right)}} + {2n\;\pi\mspace{14mu}({radian})\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}\left( {S\; 275} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 315} \right\rbrack} & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{9}{8}} \right)} + {2n\;\pi\mspace{14mu}({radian})}}} & {{Formula}\mspace{14mu}\left( {S\; 276} \right)}\end{matrix}$

In equations (S273), (S274), (S275), and (S276), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

[Mathematical  formula  316] $\begin{matrix}{{{- \frac{\pi}{2}}\mspace{14mu}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}\mspace{14mu}({radian})}} & {{Formula}\mspace{14mu}\left( {S\; 277} \right)}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S269),(S270), (S271), and (S272), and that θ is set to one of equations(S273), (S274), (S275), and (S276), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 21 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 22 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.23 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 24 . In FIGS. 21,22, 23, and24 , a horizontal axis indicates I, and a vertical axis indicates Q, amark “●” indicates a signal point, and a mark “Δ” indicates origin (0).

As can be seen from FIGS. 21, 22, 23, and 24 , the 16384 signal pointsexist while not overlapping one another. On the I-Q plane, Euclideandistances between closest signal points are equal in the 16380 signalpoints of the 16384 signal points except for the rightmost and uppermostpoint in FIG. 21 , the rightmost and lowermost point in FIG. 24 , theleftmost and uppermost point in FIG. 22 , and the leftmost and lowermostpoint in FIG. 23 . Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S269),(S270), (S271), and (S272), and that θ is set to one of equations(S273), (S274), (S275), and (S276), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 25 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 26 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.27 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 28 . In FIGS. 25, 26, 27,and 28 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 25, 26, 27, and 28 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 16384signal points in FIGS. 21, 22, 23, and 24 , and that D₂ is a minimumEuclidean distance at the 16384 signal points in FIGS. 25, 26, 27, and28 . D₁>D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁>Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 4-7

Equations (S224) and (S225) hold with respect to coefficient w₆₄ of the64QAM mapping method and coefficient w₂₅₆ of the 256QAM mapping method,and precoding matrix F is set to one of equations (S173), (S174),(S175), and (S176) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 317} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 278} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 319} \right\rbrack & \; \\{{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 279} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 321} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 280} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 321} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}} & {{Formula}\mspace{14mu}\left( {S\; 281} \right)}\end{matrix}$

In equations (S278), (S279), (S280), and (S281), α may be either a realnumber or an imaginary number, and β may be either a real number or animaginary number. However, α is not 0 (zero). Also β is not 0 (zero).

At this point, value α with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value α withwhich the receiver obtains the good data reception quality.

When α is a real number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 321} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{8}{9}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 282} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 322} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{8}{9}}} & {{Formula}\mspace{14mu}\left( {S\; 283} \right)}\end{matrix}$

When α is an imaginary number:

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 323} \right\rbrack & \; \\{{\alpha = {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{8}{9} \times e^{j\frac{\pi}{2}}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 284} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 324} \right\rbrack & \; \\{\alpha = {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{8}{9} \times e^{j\frac{3\pi}{2}}}} & {{Formula}\mspace{14mu}\left( {S\; 285} \right)}\end{matrix}$

In the case that precoding matrix F is set to one of equations (S278),(S279), (S280), and (S281), and that α is set to one of equations(S282), (S283), (S284), and (S285), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 29 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 30 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.31 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 32 . In FIGS. 29, 30, 31,and 32 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 29, 30, 31, and 32 , the 16384 signal pointsexist while not overlapping one another. On the I-Q plane, Euclideandistances between closest signal points are equal in the 16380 signalpoints of the 16384 signal points except for the rightmost and uppermostpoint in FIG. 29 , the rightmost and lowermost point in FIG. 32 , theleftmost and uppermost point in FIG. 30 , and the leftmost and lowermostpoint in FIG. 31 . Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S278),(S279), (S280), and (S281), and that α is set to one of equations(S282), (S283), (S284), and (S285), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 33 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 34 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.35 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 36 . In FIGS. 33, 34, 35,and 36 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 33, 34, 35, and 36 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 16384signal points in FIGS. 29, 30, 31, and 32 , and that D₂ is a minimumEuclidean distance at the 16384 signal points in FIGS. 33, 34, 35, and36 . D₁>D₂ holds. Accordingly, from configuration example R1, it isnecessary that |Q₁|>|Q₂| holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 4-8

Equations (S224) and (S225) hold with respect to coefficient w₆₄ of the64QAM mapping method and coefficient w₂₅₆ of the 256QAM mapping method,and precoding matrix F is set to one of equations (S173), (S174),(S175), and (S176) when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (S2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 325} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{14mu}\theta} & {\beta \times \sin\mspace{14mu}\theta} \\{\beta \times \sin\mspace{14mu}\theta} & {{- \beta} \times \cos\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 286} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 326} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\mspace{14mu}\theta} & {\sin\mspace{14mu}\theta} \\{\sin\mspace{14mu}\theta} & {{- \cos}\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 287} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 327} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{14mu}\theta} & {{- \beta} \times \sin\mspace{14mu}\theta} \\{\beta \times \sin\mspace{14mu}\theta} & {\beta \times \cos\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 288} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 328} \right\rbrack & \; \\{F = \begin{pmatrix}{\cos\mspace{14mu}\theta} & {{- \sin}\mspace{14mu}\theta} \\{\sin\mspace{14mu}\theta} & {\cos\mspace{14mu}\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}\left( {S\; 289} \right)}\end{matrix}$

In equations (S286) and (S288), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 329} \right\rbrack} & \; \\{\theta = {{{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{8}{9}} \right)}} + {2n\;\pi\mspace{14mu}({radian})\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}\left( {S\; 290} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 330} \right\rbrack} & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {\frac{\sqrt{42}}{\sqrt{170}} \times \frac{8}{9}} \right)} + {2n\;\pi\mspace{14mu}({radian})\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}\left( {S\; 291} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 331} \right\rbrack} & \; \\{\theta = {{{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{8}{9}} \right)}} + {2n\;\pi\mspace{14mu}({radian})\mspace{14mu}{or}}}} & {{Formula}\mspace{14mu}\left( {S\; 292} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 332} \right\rbrack} & \; \\{\theta = {\pi + {{\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{8}{9}} \right)}\mspace{14mu}{or}\mspace{14mu}\pi} + {\tan^{- 1}\left( {{- \frac{\sqrt{42}}{\sqrt{170}}} \times \frac{8}{9}} \right)} + {2n\;\pi\mspace{14mu}({radian})}}} & {{Formula}\mspace{14mu}\left( {S\; 293} \right)}\end{matrix}$

In equations (S290), (S291), (S292), and (S293), tan⁻¹(x) is an inversetrigonometric function) (an inverse function of a trigonometric functionin which a domain is properly restricted), and tan⁻¹(x) is given asfollows.

[Mathematical  formula  333] $\begin{matrix}{{{- \frac{\pi}{2}}\mspace{14mu}({radian})} < {\tan^{- 1}(x)} < {\frac{\pi}{2}\mspace{14mu}({radian})}} & {{Formula}\mspace{14mu}({S294})}\end{matrix}$

“tan⁻¹(x)” may also be referred to as “Tan⁻¹(x)”, “arctan(x)”, or“Arctan(x)”, and n is an integer.

In the case that precoding matrix F is set to one of equations (S286),(S287), (S288), and (S289), and that θ is set to one of equations(S290), (S291), (S292), and (S293), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 29 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 30 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.31 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 32 . In FIGS. 29, 30, 31,and 2532 , a horizontal axis indicates I, and a vertical axis indicatesQ, a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 29, 30, 31, and 32 , the 16384 signal pointsexist while not overlapping one another. On the I-Q plane, Euclideandistances between closest signal points are equal in the 16380 signalpoints of the 16384 signal points except for the rightmost and uppermostpoint in FIG. 29 , the rightmost and lowermost point in FIG. 32 , theleftmost and uppermost point in FIG. 30 , and the leftmost and lowermostpoint in FIG. 31 . Therefore, the receiver has a high possibility ofobtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S286),(S287), (S288), and (S289), and that θ is set to one of equations(S290), (S291), (S292), and (S293), in the signal points correspondingto (b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64) b_(5,64),b_(0,256), b_(1,256), b_(2,256), b_(3,256), b_(4,256), b_(5,256),b_(6,256), b_(7,256)) in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane, similarly the arrangement of the signal pointsexisting in the first quadrant is obtained as illustrated in FIG. 33 ,the arrangement of the signal points existing in the second quadrant isobtained as illustrated in FIG. 34 , the arrangement of the signalpoints existing in the third quadrant is obtained as illustrated in FIG.35 , and the arrangement of the signal points existing in the fourthquadrant is obtained as illustrated in FIG. 36 . In FIGS. 33, 34, 35,and 36 , a horizontal axis indicates I, and a vertical axis indicates Q,a mark “●” indicates a signal point, and a mark “Δ” indicates origin(0).

As can be seen from FIGS. 33, 34, 35, and 36 , the 1024 signal pointsexist while not overlapping one another. Therefore, the receiver has ahigh possibility of obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 16384signal points in FIGS. 29, 30, 31, and 32 , and that D₂ is a minimumEuclidean distance at the 16384 signal points in FIGS. 33, 34, 35, and36 . D₁>D₂ holds. Accordingly, from configuration example R1, it isnecessary that Q₁>Q₂ holds for Q₁≠Q₂ in equations (s2), (S3), (S4),(S5), and (S8).

Example 4-Supplement

Values α and θ having the possibility of achieving the high datareception quality are illustrated in (Example 4-1) to (Example 4-8).However, even if values α and θ are not those in (Example 4-1) to(Example 4-8), sometimes the high data reception quality is obtained bysatisfying the condition of configuration example R1.

Modification

A precoding method according to a modification of each of (Example 1) to(Example 4) will be described below. In FIG. 5 , it is considered thatbaseband signal 511A (z₁(t) (z₁(i))) and baseband signal 511B (z₂(t)(z₂(i))) are given by one of the following equations.

$\begin{matrix}{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 334} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\;{\theta_{11}{(i)}}}} & {\beta \times \alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\beta \times \alpha \times e^{j\;{\theta_{21}{(i)}}}} & {\beta \times e^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & {{Formula}\mspace{14mu}\left( {S\; 295} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 335} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\;{\theta_{11}{(i)}}} & {\alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times e^{j\;{\theta_{21}{(i)}}}} & e^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & {{Formula}\mspace{14mu}\left( {S\; 296} \right)}\end{matrix}$

In the formulas, θ₁₁(i) and θ₂₁(i) are a function of i (time orfrequency), λ is a fixed value, α may be either a real number or animaginary number, and β may be either a real number or an imaginarynumber. However, α is not 0 (zero). Also β is not 0 (zero).

In the modification of (Example 1), it is assumed that the modulationscheme of baseband signal 505A (s₁(t) (s₁(i))) is set to 16QAM while themodulation scheme of baseband signal 505B (s₂(t) (s₂(i))) is set to64QAM, and that equations (S11) and (S12) hold with respect tocoefficient w₁₆ of the 16QAM mapping method and coefficient w₆₄ of the64QAM mapping method.

Even if one of equations (S18), (S19), (S20), and (S21) is used in α ofequations (S295) and (S296), and even if Q₁>Q₂ holds,

or

even if one of equations (S35), (S36), (S37), and (S38) is used in α ofequations (S295) and (S296), and even if Q₁>Q₂ holds,

or

even if one of equations (S52), (S53), (S54), and (S55) is used in α ofequations (S295) and (S296), and even if Q₁<Q₂ holds,

or

even if one of equations (S69), (S70), (S71), and (S72) is used in α ofequations (S295) and (S296), and even if Q₁<Q₂ holds,

the effect similar to (Example 1) can be obtained.

In the modification of (Example 2), it is assumed that the modulationscheme of baseband signal 505A (s₁(t) (s₁(i))) is set to 64QAM while themodulation scheme of baseband signal 505B (s₂(t) (s₂(i))) is set to16QAM, and that equations (S82) and (S83) hold with respect tocoefficient w₁₆ of the 16QAM mapping method and coefficient w₆₄ of the64QAM mapping method.

even if one of equations (S89), (S90), (S91), and (S92) is used in α ofequations (S295) and (S296), and even if Q₁<Q₂ holds,

or

even if one of equations (S106), (S107), (S108), and (S109) is used in αof equations (S295) and (S296), and even if Q₁<Q₂ holds,

or

even if one of equations (S123), (S124), (S125), and (S126) is used in αof equations (S295) and (S296), and even if Q₁<Q₂ holds,

or

even if one of equations (S140), (S141), (S142), and (S143) is used in αof equations (S295) and (S296), and even if Q₁<Q₂ holds,

the effect similar to (Example 2) can be obtained.

In the modification of (Example 3), it is assumed that the modulationscheme of baseband signal 505A (s₁(t) (s₁(i))) is set to 64QAM while themodulation scheme of baseband signal 505B (s₂(t) (s₂(i))) is set to256QAM, and that equations (S153) and (S154) hold with respect tocoefficient w₆₄ of the 64QAM mapping method and coefficient w₂₅₆ of the256QAM mapping method even if one of equations (S160), (S161), (S162),and (S163) is used in α of equations (S295) and (S296), and even ifQ₁<Q₂ holds,

or

even if one of equations (S177), (S178), (S179), and (S180) is used in αof equations (S295) and (S296), and even if Q₁<Q₂ holds,

or

even if one of equations (S194), (S195), (S196), and (S197) is used in αof equations (S295) and (S296), and even if Q₁<Q₂ holds,

or

even if one of equations (S211), (S212), (S213), and (S214) is used in αof equations (S295) and (S296), and even if Q₁<Q₂ holds,

the effect similar to (Example 3) can be obtained.

In the modification of (Example 4), it is assumed that the modulationscheme of baseband signal 505A (s₁(t) (s₁(i))) is set to 256QAM whilethe modulation scheme of baseband signal 505B (s₂(t) (s₂(i))) is set to64QAM, and that equations (S224) and (S225) hold with respect tocoefficient w₆₄ of the 64QAM mapping method and coefficient w₂₅₆ of the256QAM mapping method.

even if one of equations (S231), (S232), (S233), and (S234) is used in αof equations (S295) and (S296), and even if Q₁<Q₂ holds, or

even if one of equations (S248), (S249), (S250), and (S251) is used in αof equations (S295) and (S296), and even if Q₁<Q₂ holds, or

even if one of equations (S265), (S266), (S267), and (S268) is used in αof equations (S295) and (S296), and even if Q₁>Q₂ holds, or

even if one of equations (S282), (S283), (S284), and (S285) is used in αof equations (S295) and (S296), and even if Q₁>Q₂ holds,

the effect similar to (Example 4) can be obtained.

In the above modifications, values α and θ having the possibility ofachieving the high data reception quality are illustrated. However, evenif values α and θ are not those in the modifications, sometimes the highdata reception quality is obtained by satisfying the condition ofconfiguration example R1.

An example different from (Example 1) to (Example 4) and themodification thereof will be described below.

Example 5

In mapper 504 of FIGS. 5 to 7 , the modulation scheme for obtainings₁(t) (s₁(i)) is set to 16QAM while the modulation scheme for obtainings₂(t) (s₂(i)) is set to 64QAM. An example of conditions associated withthe configuration and power change of precoding matrix (F) when theprecoding and/or the power change is performed on, for example, one ofequations (s2), (S3), (S4), (S5), and (S8) will be described below.

The 16QAM mapping method will be described below. FIG. 10 illustrates anarrangement example of 16QAM signal points in the I-Q plane. In FIG. 10, 16 marks “◯” indicate 16QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 16 signal points included in 16QAM (indicated by themarks “◯” in FIG. 10 ) are obtained as follows. (w₁₆ is a real numberlarger than 0)

(3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆), (3w₁₆,−3w₁₆), (w₁₆,3w₁₆),(w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆), (−w₁₆,3w₁₆), (−w₁₆,w₁₆),(−w₁₆,−w₁₆), (−w₁₆,−3w₁₆), (−3w₁₆,3w₁₆), (−3w₁₆,w₁₆), (−3w₁₆,−w₁₆),(−3w₁₆,−3w₁₆)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, and b3. For example, in the case that the bits to be transmittedis (b0, b1, b2, b3)=(0,0,0,0), the bits are mapped at signal point 1001in FIG. 10 , and (I,Q)=(3w₁₆,3w₁₆) is obtained when I is an in-phasecomponent while Q is a quadrature component of the mapped basebandsignal.

Based on the bits to be transmitted (b0, b1, b2, b3), in-phase componentI and quadrature component Q of the mapped baseband signal are decided(during 16QAM modulation). FIG. 10 illustrates an example of therelationship between the set of b0, b1, b2, and b3 (0000 to 1111) andthe signal point coordinates. Values 0000 to 1111 of the set of b0, b1,b2, and b3 are indicated immediately below 16 signal points included in16QAM (the marks “◯” in FIG. 10 ) (3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆),(3w₁₆,−3w₁₆), (w₁₆,3w₁₆), (w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆),(−w₁₆,3w₁₆), (−w₁₆,w₁₆), (−w₁₆,−w₁₆), (−w₁₆,−3w₁₆), (−3w₁₆,3w₁₆),(−3w₁₆,w₁₆), (−3w₁₆,−w₁₆), (−3w₁₆,−3w₁₆). Respective coordinates of thesignal points (“◯”) immediately above the values 0000 to 1111 of the setof b0, b1, b2, and b3 in the I-Q plane serve as in-phase component I andquadrature component Q of the mapped baseband signal. The relationshipbetween the set of b0, b1, b2, and b3 (0000 to 1111) and the signalpoint coordinates during 16QAM modulation is not limited to that in FIG.10 . A complex value of in-phase component I and quadrature component Qof the mapped baseband signal (during 16QAM modulation) serves as abaseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7 ).

The 64QAM mapping method will be described below. FIG. 11 illustrates anarrangement example of 64QAM signal points in the I-Q plane. In FIG. 11, 64 marks “◯” indicate 64QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 64 signal points included in 64QAM (indicated by themarks “◯” in FIG. 11 ) are obtained as follows. (w₆₄ is a real numberlarger than 0)

(7w₆₄,7w₆₄), (7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄),(7w₆₄,−3w₆₄), (7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄)

(−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄), (−w₆₄,w₆₄), (−w₆₄,−w₆₄),(−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, in the case that the bits to betransmitted is (b0, b1, b2, b3, b4, b5)=(0,0,0,0,0,0), the bits aremapped at signal point 1101 in FIG. 11 , and (I,Q)=(7w₆₄,7w₆₄) isobtained when I is an in-phase component while Q is a quadraturecomponent of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 11 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to of the set ofb0, b1, b2, b3, b4, and b5 are indicated immediately below 64 signalpoints included in 64QAM (the marks “◯” in FIG. 11 ) (7w₆₄,7w₆₄),(7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄), (7w₆₄,−3w₆₄),(7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄)

(−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄), (−w₆₄,w₆₄), (−w₆₄,−w₆₄),(−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄). Respective coordinates ofthe signal points (“◯”) immediately above the values 000000 to 111111 ofthe set of b0, b1, b2, b3, b4, and b5 in the I-Q plane serve as in-phasecomponent I and quadrature component Q of the mapped baseband signal.The relationship between the set of b0, b1, b2, b3, b4, and b5 (000000to 111111) and the signal point coordinates during 64QAM modulation isnot limited to that in FIG. 11 . A complex value of in-phase component Iand quadrature component Q of the mapped baseband signal (during 64QAMmodulation) serves as a baseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7).

In this case, the modulation scheme of baseband signal 505A (s₁(t)(s₁(i))) is set to 16QAM while modulation scheme of baseband signal 505B(s₂(t) (s₂(i))) is set to 64QAM in FIG. 5 to FIG. 7 . The configurationof the precoding matrix will be described below.

At this point, generally average power of baseband signal 505A (s₁(t)and (s₁(i))) and average power of baseband signal 505B (s₂(t) and(s₂(i))), which are of the output of mapper 504 in FIGS. 5 to 7 , areequalized to each other. Accordingly, equations (S11) and (S12) holdwith respect to coefficient w₁₆ of the 16QAM mapping method andcoefficient w₆₄ of the 64QAM mapping method. In equations (S11) and(S12), it is assumed that z is a real number larger than 0. When thecalculations are performed in <1> to <5>,

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

the configuration of precoding matrix F and a relationship between Q₁and Q₂ will be described below.

Equations (S11) and (S12) hold with respect to coefficient w₁₆ of the16QAM mapping method and coefficient w₆₄ of the 64QAM mapping method,and one of equations (S22), (S23), (S24), and (S25) is considered asprecoding matrix F when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

In equations (S22) and (S24), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₁(t) (z₁(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 336} \right\rbrack & \; \\{{\theta = {{15\mspace{14mu}{or}\mspace{14mu} 15} + {360 \times n\mspace{14mu}({degree})}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 297} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 337} \right\rbrack & \; \\{{{\begin{matrix}{\theta = {180 + 15}} \\{= 195}\end{matrix}\mspace{14mu}{or}\mspace{14mu} 195} + {360 \times n\mspace{14mu}({degree})}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 298} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 338} \right\rbrack & \; \\{{\theta = {{{- 15}\mspace{14mu}{or}}\mspace{14mu} - 15 + {360 \times n\mspace{14mu}({degree})}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 299} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 338} \right\rbrack & \; \\{{\begin{matrix}{\theta = {180 - 15}} \\{= 165}\end{matrix}\mspace{14mu}{or}\mspace{14mu} 165} + {360 \times n\mspace{14mu}({degree})}} & {{Formula}\mspace{14mu}\left( {S\; 300} \right)}\end{matrix}$

In the formulas, n is an integer.

In the case that precoding matrix F is set to one of equations (S22),(S23), (S24), and (S25), and that θ is set to one of equations (S297),(S298), (S299), and (S300), similarly the arrangement of the signalpoint at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 55 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 55 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 55 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S22),(S23), (S24), and (S25), and that θ is set to one of equations (S297),(S298), (S299), and (S300), similarly the arrangement of the signalpoint at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 56 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 56 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 56 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₁ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 55 , and that D₂ is a minimum Euclidean distance at the1024 signal points in FIG. 56 . D₁>D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁>Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 5-Supplement

Value θ having the possibility of achieving the high data receptionquality are illustrated in (Example 5). However, even if value θ is notone in (Example 5), sometimes the high data reception quality isobtained by satisfying the condition of configuration example R1.

Example 6

In mapper 504 of FIGS. 5 to 7 , the modulation scheme for obtainings₁(t) (s₁(i)) is set to 64QAM while the modulation scheme for obtainings₂(t) (s₂(i)) is set to 16QAM. An example of conditions associated withthe configuration and power change of precoding matrix (F) when theprecoding and/or the power change is performed on, for example, one ofequations (s2), (S3), (S4), (S5), and (S8) will be described below.

The 16QAM mapping method will be described below. FIG. 10 illustrates anarrangement example of 16QAM signal points in the I-Q plane. In FIG. 10, 16 marks “◯” indicate 16QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 16 signal points included in 16QAM (indicated by themarks “◯” in FIG. 10 ) are obtained as follows. (w₁₆ is a real numberlarger than 0)

(3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆), (3w₁₆,−3w₁₆), (w₁₆,3w₁₆),(w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆), (−w₁₆,3w₁₆), (−w₁₆,w₁₆),(−w₁₆,−w₁₆), (−w₁₆,−3w₁₆), (−3w₁₆,3w₁₆), (−3w₁₆,w₁₆), (−3w₁₆,−w₁₆),(−3w₁₆,−3w₁₆)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, and b3. For example, in the case that the bits to be transmittedis (b0, b1, b2, b3)=(0,0,0,0), the bits are mapped at signal point 1001in FIG. 10 , and (I,Q)=(3w₁₆,3w₁₆) is obtained when I is an in-phasecomponent while Q is a quadrature component of the mapped basebandsignal.

Based on the bits to be transmitted (b0, b1, b2, b3), in-phase componentI and quadrature component Q of the mapped baseband signal are decided(during 16QAM modulation). FIG. 10 illustrates an example of therelationship between the set of b0, b1, b2, and b3 (0000 to 1111) andthe signal point coordinates. Values 0000 to 1111 of the set of b0, b1,b2, and b3 are indicated immediately below 16 signal points included in16QAM (the marks “◯” in FIG. 10 ) (3w₁₆,3w₁₆), (3w₁₆,w₁₆), (3w₁₆,−w₁₆),(3w₁₆,−3w₁₆), (w₁₆,3w₁₆), (w₁₆,w₁₆), (w₁₆,−w₁₆), (w₁₆,−3w₁₆),(−w₁₆,3w₁₆), (−w₁₆,w₁₆), (−w₁₆,−w₁₆), (−w₁₆,−3w₁₆), (−3w₁₆,3w₁₆),(−3w₁₆,w₁₆), (−3w₁₆,−w₁₆), (−3w₁₆,−3w₁₆). Respective coordinates of thesignal points (“◯”) immediately above the values 0000 to 1111 of the setof b0, b1, b2, and b3 in the I-Q plane serve as in-phase component I andquadrature component Q of the mapped baseband signal. The relationshipbetween the set of b0, b1, b2, and b3 (0000 to 1111) and the signalpoint coordinates during 16QAM modulation is not limited to that in FIG.10 . A complex value of in-phase component I and quadrature component Qof the mapped baseband signal (during 16QAM modulation) serves as abaseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7 ).

The 64QAM mapping method will be described below. FIG. 11 illustrates anarrangement example of 64QAM signal points in the I-Q plane. In FIG. 11, 64 marks “◯” indicate 64QAM signal points, a horizontal axis indicatesI, and a vertical axis indicates Q.

In the I-Q plane, 64 signal points included in 64QAM (indicated by themarks “◯” in FIG. 11 ) are obtained as follows. (w₆₄ is a real numberlarger than 0)

(7w₆₄,7w₆₄), (7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄),(7w₆₄,−3w₆₄), (7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄)

(−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄), (−w₆₄,w₆₄), (−w₆₄,−w₆₄),(−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄,−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄)

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, in the case that the bits to betransmitted is (b0, b1, b2, b3, b4, b5)=(0,0,0,0,0,0), the bits aremapped at signal point 1101 in FIG. 11 , and (I,Q)=(7w₆₄,7w₆₄) isobtained when I is an in-phase component while Q is a quadraturecomponent of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 11 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to 111111 of theset of b0, b1, b2, b3, b4, and b5 are indicated immediately below 64signal points included in 64QAM (the marks “◯” in FIG. 11 ) (7w₆₄,7w₆₄),(7w₆₄,5w₆₄), (7w₆₄,3w₆₄), (7w₆₄,w₆₄), (7w₆₄,−w₆₄), (7w₆₄,−3w₆₄),(7w₆₄,−5w₆₄), (7w₆₄,−7w₆₄)

(5w₆₄,7w₆₄), (5w₆₄,5w₆₄), (5w₆₄,3w₆₄), (5w₆₄,w₆₄), (5w₆₄,−w₆₄),(5w₆₄,−3w₆₄), (5w₆₄,−5w₆₄), (5w₆₄,−7w₆₄)

(3w₆₄,7w₆₄), (3w₆₄,5w₆₄), (3w₆₄,3w₆₄), (3w₆₄,w₆₄), (3w₆₄,−w₆₄),(3w₆₄,−3w₆₄), (3w₆₄,−5w₆₄), (3w₆₄,−7w₆₄)

(w₆₄,7w₆₄), (w₆₄,5w₆₄), (w₆₄,3w₆₄), (w₆₄,w₆₄), (w₆₄,−w₆₄), (w₆₄,−3w₆₄),(w₆₄,−5w₆₄), (w₆₄,−7w₆₄)

(−w₆₄,7w₆₄), (−w₆₄,5w₆₄), (−w₆₄,3w₆₄), (−w₆₄,w₆₄), (−w₆₄,−w₆₄),(−w₆₄,−3w₆₄), (−w₆₄,−5w₆₄), (−w₆₄,−7w₆₄)

(−3w₆₄,7w₆₄), (−3w₆₄,5w₆₄), (−3w₆₄,3w₆₄), (−3w₆₄,w₆₄), (−3w₆₄,−w₆₄),(−3w₆₄,−3w₆₄), (−3w₆₄,−5w₆₄), (−3w₆₄,−7w₆₄)

(−5w₆₄,7w₆₄), (−5w₆₄,5w₆₄), (−5w₆₄,3w₆₄), (−5w₆₄,w₆₄), (−5w₆₄,−w₆₄),(−5w₆₄,−3w₆₄), (−5w₆₄,−5w₆₄), (−5w₆₄,−7w₆₄)

(−7w₆₄,7w₆₄), (−7w₆₄,5w₆₄), (−7w₆₄,3w₆₄), (−7w₆₄,w₆₄), (−7w₆₄,−w₆₄),(−7w₆₄,−3w₆₄), (−7w₆₄,−5w₆₄), (−7w₆₄,−7w₆₄). Respective coordinates ofthe signal points (“◯”) immediately above the values 000000 to 111111 ofthe set of b0, b1, b2, b3, b4, and b5 in the I-Q plane serve as in-phasecomponent I and quadrature component Q of the mapped baseband signal.The relationship between the set of b0, b1, b2, b3, b4, and b5 (000000to 111111) and the signal point coordinates during 64QAM modulation isnot limited to that in FIG. 11 . A complex value of in-phase component Iand quadrature component Q of the mapped baseband signal (during 64QAMmodulation) serves as a baseband signal (s₁(t) or s₂(t) in FIGS. 5 to 7).

In this case, the modulation scheme of baseband signal 505A (s₁(t)(s₁(i))) is set to 64QAM while modulation scheme of baseband signal 505B(s₂(t) (s₂(i))) is set to 16QAM in FIG. 5 to FIG. 7 . The configurationof the precoding matrix will be described below.

At this point, generally average power of baseband signal 505A (s₁(t)and (s₁(i))) and average power of baseband signal 505B (s₂(t) and(s₂(i))), which are of the output of mapper 504 in FIGS. 5 to 7 , areequalized to each other. Accordingly, equations (S82) and (S83) holdwith respect to coefficient w₁₆ of the 16QAM mapping method andcoefficient w₆₄ of the 64QAM mapping method. In equations (S82) and(S83), it is assumed that z is a real number larger than 0. When thecalculations are performed in <1> to <5>,

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

the configuration of precoding matrix F and a relationship between Q₁and Q₂ will be described below.

Equations (S11) and (S12) hold with respect to coefficient w₁₆ of the16QAM mapping method and coefficient w₆₄ of the 64QAM mapping method,and one of equations (S93), (S94), (S95), and (S96) is considered asprecoding matrix F when the calculations are performed in <1> to <5>.

<1> For P₁ ²=P₂ ² in equation (s2)

<2> For P₁ ²=P₂ ² in equation (S3)

<3> For P₁ ²=P₂ ² in equation (S4)

<4> For equation (S5)

<5> For equation (S8)

In equations (S93) and (S95), β may be either a real number or animaginary number. However, β is not 0 (zero).

At this point, value θ with which the receiver obtains the good datareception quality is considered.

With respect to signal z₂(t) (z₂(i)) in equations (s2), (S3), (S4),(S5), and (S8), the following equations are considered as value θ withwhich the receiver obtains the good data reception quality.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 340} \right\rbrack & \; \\{{\theta = {{15\mspace{14mu}{or}\mspace{14mu} 15} + {360 \times n\mspace{14mu}({degree})}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 301} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 341} \right\rbrack & \; \\{{{\begin{matrix}{\theta = {180 + 15}} \\{= 195}\end{matrix}\mspace{14mu}{or}\mspace{14mu} 195} + {360 \times n\mspace{14mu}({degree})}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 302} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 342} \right\rbrack & \; \\{{\theta = {{{- 15}\mspace{14mu}{or}}\mspace{14mu} - 15 + {360 \times n\mspace{14mu}({degree})}}}{or}} & {{Formula}\mspace{14mu}\left( {S\; 303} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 343} \right\rbrack & \; \\{{\begin{matrix}{\theta = {180 - 15}} \\{= 165}\end{matrix}\mspace{14mu}{or}\mspace{14mu} 165} + {360 \times n\mspace{14mu}({degree})}} & {{Formula}\mspace{14mu}\left( {S\; 304} \right)}\end{matrix}$

In the formulas, n is an integer.

In the case that precoding matrix F is set to one of equations (S93),(S94), (S95), and (S96), and that θ is set to one of equations (S301),(S302), (S303), and (S304), similarly the arrangement of the signalpoint at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 55 in signal u₂(t) (u₂(i)) of configuration exampleR1 on the I-Q plane. In FIG. 55 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 55 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

In the case that precoding matrix F is set to one of equations (S93),(S94), (S95), and (S96), and that θ is set to one of equations (S301),(S302), (S303), and (S304), similarly the arrangement of the signalpoint at which (b_(0,16), b_(1,16), b_(2,16), b_(3,16), b_(0,64),b_(1,64), b_(2,64), b_(3,64), b_(4,64), b_(5,64)) corresponds to(0,0,0,0,0,0,0,0,0,0) to the signal point at which (b_(0,16), b_(1,16),b_(2,16), b_(3,16), b_(0,64), b_(1,64), b_(2,64), b_(3,64), b_(4,64),b_(5,64)) corresponds to (1,1,1,1,1,1,1,1,1,1) is obtained asillustrated in FIG. 56 in signal u₁(t) (u₁(i)) of configuration exampleR1 on the I-Q plane. In FIG. 56 , a horizontal axis indicates I, and avertical axis indicates Q, and a mark “●” indicates a signal point.

As can be seen from FIG. 56 , the 1024 signal points exist while notoverlapping one another. Therefore, the receiver has a high possibilityof obtaining the high reception quality.

It is assumed that D₂ is a minimum Euclidean distance at the 1024 signalpoints in FIG. 55 , and that D₁ is a minimum Euclidean distance at the1024 signal points in FIG. 56 . D₁<D₂ holds. Accordingly, fromconfiguration example R1, it is necessary that Q₁<Q₂ holds for Q₁≠Q₂ inequations (s2), (S3), (S4), (S5), and (S8).

Example 6-Supplement

Value θ having the possibility of achieving the high data receptionquality are illustrated in (Example 6). However, even if value θ is notone in (Example 6), sometimes the high data reception quality isobtained by satisfying the condition of configuration example R1.

The operation of the receiver in the case that the transmitter transmitsthe modulated signal using (Example 1) to (Example 4) and themodulations thereof, (Example 5), and (Example 6) will be describedbelow.

FIG. 53 illustrates the relationship between the transmitting antennaand the receiving antenna. It is assumed that modulated signal #1(S4901A) is transmitted from transmitting antenna #1 (S4902A) of thetransmitter, and that modulated signal #2 (S4901B) is transmitted fromantenna #2 (S4902B).

Receiving antenna #1 (S4903X) and receiving antenna #2 (S4903Y) of thereceiver receive the modulated signals transmitted from the transmitter(obtain received signal S490X and received signal S4904Y). At thispoint, it is assumed that h₁₁(t) is a propagation coefficient fromtransmitting antenna #1 (S4902A) from receiving antenna #1 (S4903X),that h₂₁(t) is a propagation coefficient from transmitting antenna #1(4902A) to receiving antenna #2 (4903Y), that h₁₂(t) is a propagationcoefficient from transmitting antenna #2 (S4902B) to receiving antenna#1 (S4903X), and that h₂₂(t) is a propagation coefficient fromtransmitting antenna #2 (S4902B) to receiving antenna #2 (S4903Y) (t istime).

FIG. 54 illustrates a configuration example of the receiver. Receivedsignal 5401X received by receiving antenna #1 (S4903X) is input to radiosection 5402X, and radio section 5402X performs the pieces of processingsuch as the amplification and the frequency conversion to output signal5403X.

For example, when the OFDM scheme is used, signal processor 5404Xperforms the pieces of processing such as a Fourier transform and aparallel-serial conversion to obtain baseband signal 5405X. At thispoint, baseband signal 5405X is represented as r′₁(t).

Received signal 5401Y received by receiving antenna #2 (S4903Y) is inputto radio section 5402Y, and radio section 5402Y performs the pieces ofprocessing such as the amplification and the frequency conversion tooutput signal 5403Y.

For example, when the OFDM scheme is used, signal processor 5404Yperforms the pieces of processing such as a Fourier transform and aparallel-serial conversion to obtain baseband signal 5405Y. At thispoint, baseband signal 5405Y is represented as r′₂(t).

Baseband signal 5405X is input to channel estimator 5406X, and channelestimator 5406X performs the channel estimation (estimation of thepropagation coefficient) from, for example, the pilot symbol of theframe configuration in FIG. 9 to output channel estimation signal 5407X.It is assumed that channel estimation signal 5407X is an estimatedsignal of h₁₁(t) and represented as h′₁₁(t).

Baseband signal 5405X is input to channel estimator 5408X, and channelestimator 5408X performs the channel estimation (estimation of thepropagation coefficient) from, for example, the pilot symbol of theframe configuration in FIG. 9 to output channel estimation signal 5409X.It is assumed that channel estimation signal 5409X is an estimatedsignal of h₁₂(t) and represented as h′₁₂(t).

Baseband signal 5405Y is input to channel estimator 5406Y, and channelestimator 5406Y performs the channel estimation (estimation of thepropagation coefficient) from, for example, the pilot symbol of theframe configuration in FIG. 9 to output channel estimation signal 5407Y.It is assumed that channel estimation signal 5407Y is an estimatedsignal of h₂₁(t) and represented as h′₂₁(t).

Baseband signal 5405Y is input to channel estimator 5408Y, and channelestimator 5408Y performs the channel estimation (estimation of thepropagation coefficient) from, for example, the pilot symbol of theframe configuration in FIG. 9 to output channel estimation signal 5409Y.It is assumed that channel estimation signal 5409Y is an estimatedsignal of h₂₂(t) and represented as h′₂₂(t).

Baseband signal 5005X and baseband signal 540Y are input to controlinformation demodulator 5410, and control information demodulator 5410demodulates (detects and decodes) the symbol that transmits controlinformation including the transmission method, modulation scheme, andinformation about the transmission power, which are transmitted from thetransmitter together with the data (symbol), and control informationdemodulator 5410 outputs control information 5411.

The transmitter transmits the modulated signal by one of the abovetransmission methods. Accordingly, the transmission method fortransmitting the modulated signal is one of the following methods.

<1> Transmission method for equation (s2)

<2> Transmission method for equation (S3)

<3> Transmission method for equation (S4)

<4> Transmission method for equation (S5)

<5> Transmission method for equation (S6)

<6> Transmission method for equation (S7)

<7> Transmission method for equation (S8)

<8> Transmission method for equation (S9)

<9> Transmission method for equation (S10)

<10> Transmission method for equation (S295)

<11> Transmission method for equation (S296)

The following relationship holds in the case that the transmissionmethod for equation (s2) is used.

     [Mathematical  formula  344] $\begin{matrix}\begin{matrix}{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}}} \\{= {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}}} \\{= {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}\end{matrix} & ({S305})\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S3) is used.

[Mathematical  formula  345] $\begin{matrix}\begin{matrix}{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}}} \\{= {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}}} \\{= {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}\end{matrix} & ({S306})\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S4) is used.

[Mathematical  formula  346] $\begin{matrix}\begin{matrix}{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}}} \\{= {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}}} \\{= {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}\end{matrix} & ({S307})\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S5) is used.

[Mathematical  formula  347] $\begin{matrix}\begin{matrix}{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}}} \\{= {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}\end{matrix} & ({S308})\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S6) is used.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 348} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & ({S309})\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S7) is used.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 349} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & ({S310})\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S8) is used.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 350} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}} = {{\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & ({S311})\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S9) is used.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 351} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & ({S312})\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S10) is used.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 352} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}{a(i)} & {b(i)} \\{c(i)} & {d(i)}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & ({S313})\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S295) is used.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 353} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}{\beta \times e^{j\;{\theta_{11}{(i)}}}} & {\beta \times \alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\beta \times \alpha \times e^{j\;{\theta_{21}{(i)}}}} & {\beta \times e^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & {{Formula}\mspace{14mu}({S314})}\end{matrix}$

The following relationship holds in the case that the transmissionmethod for equation (S296) is used.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 354} \right\rbrack} & \; \\{\begin{pmatrix}{r_{1}^{\prime}(i)} \\{r_{2}^{\prime}(i)}\end{pmatrix} = {{\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix}} = {\begin{pmatrix}{h_{11}^{\prime}(i)} & {h_{12}^{\prime}(i)} \\{h_{21}^{\prime}(i)} & {h_{22}^{\prime}(i)}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\;{\theta_{11}{(i)}}} & {\alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times e^{j\;{\theta_{21}{(i)}}}} & e^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}} & {{Formula}\mspace{14mu}({S315})}\end{matrix}$

Baseband signals 5405X and 5405Y, channel estimation signals 5407X,5409X, 5407Y, and 5409Y, and control information 5411 are input todetector 5412. Based on control information 5411, detector 5412recognizes which one of the relational expressions of equations (S305),(S306), (S307), (S308), (S309), (S310), (S311), (S312), (S313), (S314),and (S315) holds.

Based on one of the relational expressions of equations (S305), (S306),(S307), (S308), (S309), (S310), (S311), (S312), (S313), (S314), and(S315), detector 5412 detects each bit of the data transmitted by s₁(t)(s₁(i)) and s₂(t) (s₂(i)) (the log-likelihood of each bit or thelog-likelihood ratio of each bit), and outputs detection result 5413.

Detection result 5413 is input to decoder 5414, and decoder 5414 decodesthe error correction code to output received data 5415.

In the configuration example, the precoding method in the MIMOtransmission scheme and the configurations of the transmitter andreceiver in which the precoding method is adopted are described above.When the precoding method is adopted, the receiver can obtain the highdata reception quality.

Each of the transmitting antenna and receiving antenna in theconfiguration examples may be one antenna unit constructed with theplurality of antennas. The plurality of antennas that transmit the twopost-precoding modulated signals may be used so as to simultaneouslytransmit one modulated signal at different times.

The receiver including the two receiving antennas is described above.Alternatively, the received data can be obtained even if the receiverincludes at least three receiving antennas.

The precoding method of the configuration example can also be performedwhen the single-carrier scheme, the OFDM scheme, the multi-carrierscheme such as the OFDM scheme in which a wavelet transformation isused, and a spread spectrum scheme are applied.

The above transmission method, reception method, transmitter, andreceiver of each configuration example are only an example of theconfiguration to which the disclosure described in each of the followingexemplary embodiments is applicable. The disclosure described in each ofthe following exemplary embodiments is also applicable to a transmissionmethod, a reception method, a transmitter, and a receiver, which aredifferent from the above transmission method, reception method,transmitter, and receiver of each configuration example.

First to Fourth Exemplary Embodiments

In the following exemplary embodiments, modifications of the processingperformed in and/or before and after the encoder and mapper of(configuration example R1) or (configuration example S1) will bedescribed. Sometimes the configuration including the encoder and themapper is also referred to as a BICM (Bit Interleaved Coded Modulation).

First complex signal s1 (s₁(t), s1(f), or s1(t,f) (t is time and f is afrequency)) is a baseband signal represented by in-phase component I andquadrature component Q based on the mapping of a certain modulationscheme such as BPSK (Binary Phase Shift Keying), QPSK (Quadrature PhaseShift Keying), 16QAM (16 Quadrature Amplitude Modulation), 64QAM (64Quadrature Amplitude Modulation), and 256QAM (256 Quadrature AmplitudeModulation). Similarly, second complex signal s2 (s₂(t), s2(f), ors2(t,f)) is a baseband signal represented by in-phase component I andquadrature component Q based on the mapping of a certain modulationscheme such as BPSK (Binary Phase Shift Keying), QPSK (Quadrature PhaseShift Keying), 16QAM (16 Quadrature Amplitude Modulation), 64QAM (64Quadrature Amplitude Modulation), and 256QAM (256 Quadrature AmplitudeModulation).

The second bit string is input to mapper 504. (X+Y) bit strings areinput to mapper 504. Using a number of first bits X in the (X+Y) bitstrings, mapper 504 generates first complex signal s₁ based on themapping of a first modulation scheme. Similarly, using a number ofsecond bits Y in the (X+Y) bit strings, mapper 504 generates secondcomplex signal s2 based on the mapping of a second modulation scheme.

In the following exemplary embodiments, after the stage of mapper 504,the specific precoding described in (configuration example R1) and(configuration example S1) may be performed, or the precoding given byone of equations (R2), (R3), (R4), (R5), (R6), (R7), (R8), (R9), (R10),(s2), (S3), (S4), (S5), (S6), (S7), (S8), (S9), and (S10) may beperformed.

Encoder 502 performs the coding (of the error correction code) from aK-bit information bit string, and outputs first bit string (503) that isof an N-bit code word. Accordingly, in this case, it is assumed that anN-bit code word, namely, a block code having an N-bit block length (codelength) is used. Examples of the block code include an LDPC (block) codedescribed in NPLs 1 and 6, a turbo code in which tail-biting is used, aDuo-Binary Turbo code described in NPLs 3 and 4 in which the tail-bitingis used, and a code described in NPL 5 in which the LDPC (block) codeand BCH code (Bose-Chaudhuri-Hocquenghem code) are coupled.

K and N are a natural number, and a relationship of N>K holds. In asystematic code used in the LDPC code, the K-bit information bit stringis included in the first bit string.

Depending on the value of the number of bits (X+Y), sometimes the codeword length (N bits) that is of the output of the encoder is not amultiple of the number of bits (X+Y) used to generate two complexsignals s1 and s2.

For example, it is assumed that code word length N has 64800 bits, 64QAMis used as the modulation scheme, and X=6 holds, or 256QAM is used asthe modulation scheme and Y=8 and X+Y=14 hold. Alternatively, forexample, it is assumed that code word length N has 16200 bits, 256QAM isused as the modulation scheme, and X=8 holds, or 256QAM is used as themodulation scheme and Y=8 and X+Y=16 hold.

In both the cases, the code word length (N bits) that is of the outputof the encoder is not a multiple of the number of bits (X+Y) used togenerate two complex signals s1 and s2.

In following exemplary embodiments, even if the code word output fromthe encoder has any length (N bits), the adjustment is performed suchthat the mapper performs processing without leaving the number of bits.

An advantage of the case that the code word length (N bits) that is ofthe output of the encoder is a multiple of the number of bits (X+Y) usedto generate two complex signals s1 and s2 will be described assupplement.

A method in which the transmitter efficiently transmits one block of theerror correction code having the N-bit code word length used in thecoding is considered. There is a higher possibility of being able toreduce a memory of the transmitter and/or receiver in the case where thenumber of bits (X+Y) transmitted by first and second complex signals s1and s2 at the identical frequency and the identical time is notconstructed with the bits of the plurality of blocks.

For (modulation scheme of first complex signal s1, modulation scheme ofsecond complex signal s2)=(16QAM,16QAM), the number of bits (X+Y) of 8bits can be transmitted by first and second complex signals s1 and s2 atthe identical frequency and the identical time, and the 8 bitspreferably do not include data of the plurality of blocks (of the errorcorrection code). That is, in the modulation scheme selected by thetransmitter, the number of bits (X+Y) transmitted by first and secondcomplex signals s1 and s2 at the identical frequency and the identicaltime preferably does not include data of the plurality of blocks (of theerror correction code).

Accordingly, the code word length (N bits) that is of the output of theencoder is preferably a multiple of the number of bits (X+Y) used togenerate two complex signals s₁ and s2.

In the transmitter, there is a high possibility of being able to switchthe plurality of modulation schemes in both the modulation schemes offirst and second complex signals s1 and s2. Accordingly, the number ofbits (X+Y) has a high possibility of taking a plurality of values.

At this point, “the code word length (N bits) that is of the output ofthe encoder is a multiple of the number of bits (X+Y) used to generatetwo complex signals s1 and s2” is not always satisfied in all the valuesthat can be taken by the number of bits (X+Y). Accordingly, processingmethods of the following exemplary embodiments are required. Theprocessing methods will be described below.

First Exemplary Embodiment

FIG. 57 illustrates a section that generates the modulated signal in atransmitter (hereinafter, the section is referred to as a modulator)according to a first exemplary embodiment. In FIG. 57 , the function andsignal identical to those of “the section that generates the modulatedsignal” described in configuration example R1 are designated by theidentical reference marks.

The modulator of the first exemplary embodiment includes bit lengthadjuster 5701 disposed between encoder 502 and mapper 504.

Encoder 502 outputs first bit string (503) that is of an N-bit code word(block length (code length)) from a K-bit information bit stringaccording to control signal 512.

Mapper 504 selects the first modulation scheme that is of the modulationscheme used to generate complex signal s₁(t) and the second modulationscheme that is of the modulation scheme used to generate complex signals₂(t) according to control signal 512. First and second complex signalss₁(t) and s₂(t) are generated using the bit string of the number of bits(X+Y), which is obtained from the number of first bits X used togenerate first complex signal s1 and the number of second bits Y used togenerate second complex signal s2 in input second bit string 5703 (asdescribed above in detail).

Bit length adjuster 5701 is located at a subsequent stage of encoder 502and a preceding stage of mapper 504. First bit string 503 is input tobit length adjuster 5701, and bit length adjuster 5701 adjusts the bitlength (in this case, the code word length (block length (code length))of the code word (block) of the error correction code) of first bitstring 503 to generate second bit string 5703.

FIG. 58 is a flowchart illustrating bit length adjustment processing ina modulation processing method of the first exemplary embodiment.

A controller (not illustrated) acquires the number of bits (X+Y) whichis obtained from the number of first bits X used to generate firstcomplex signal s1 and the number of second bits Y used to generatesecond complex signal s2 (step S5801).

The controller determines whether the code word length (block length(code length)) of the code word (block) of the error correction codeneeds to be adjusted (S5803). Whether N bits of the code word length(block length (code length)) of the error correction code are a multipleof the value of (X+Y) can be used as a criterion. Alternatively, thedetermination may be made using an association table between the valueof (X+Y) and the number of bits X. The information about (X+Y) may beinformation about the first modulation scheme that is of the modulationscheme used to generate complex signal s₁(t) and the second modulationscheme that is of the modulation scheme used to generate complex signals₂(t).

If the code word length (block length (code length)) N of the errorcorrection code is 64800 bits and the value of (X+Y) is 16, the codeword length N bits of the error correction code are a multiple of thevalue of (X+Y). The controller determines that the bit length does notneed to be adjusted (NO in S5803).

When determining that the necessity of the adjustment of the bit lengthis eliminated (NO in S5803), the controller sets bit length adjuster5701 such that bit length adjuster 5701 directly outputs input first bitstring 503 as second bit string 5703 (S5805). That is, in bit lengthadjuster 5701, the 64800-bit code word of the error correction codeserves as the input, and the 64800-bit code word of the error correctioncode serves as the output (bit length adjuster 5701 directly outputsinput bit string 503 to the mapper as second bit string 5703).

If the code word length (block length (code length)) N of the errorcorrection code is 64800 bits and the value of (X+Y) is 14, the codeword length N bits of the error correction code are not a multiple ofthe value of (X+Y). In this case, the controller determines that the bitlength needs to be adjusted (YES in S5803).

When determining that the bit length needs to be adjusted, thecontroller sets bit length adjuster 5701 such that bit length adjuster5701 performs bit length adjustment processing on input first bit string503 (S5805).

FIG. 59 is a flowchart illustrating the bit length adjustment processingof the first exemplary embodiment.

The controller decides value PadNum corresponding to how many bits needsto be adjusted for first bit string 503 (S5901). That is, the number ofbits to be added to the N bits of the code word length of the errorcorrection code constitutes PadNum.

In the first exemplary embodiment, a number equal to a value derivedfrom the following numerical expression (shortage) is decided as thevalue of PadNum (bits).PadNum=ceil(N/(X+Y))×(X+Y)−N

In the expression, the ceil function is one that returns an integer inwhich figures after a decimal point are rounded up.

The decision processing may be performed by either the calculation orthe use of a value stored in a table as long as a result equal to thevalue of the above equation is obtained.

For example, the number of bits (the value of PadNum) in which theadjustment is required may be previously stored with respect to thecontrol signal (the code word length (block length (code length) of theerror correction code), a set of the information about the modulationscheme used to generate s1 and the information about the modulationscheme used to generate s2), and the value of PadNum corresponding tothe current value of (X+Y) may be decided as the number of bits in whichthe adjustment is required. Any index value such as a coding rate and avalue of power imbalance may be used in the table as long as the numberof bits to be adjusted is obtained according to the relationship betweencode word length (block length (code length)) N of the error correctioncode and the value of (X+Y).

The above control is particularly required in a communication system inwhich the modulation scheme used to generate s1 and the modulationscheme used to generate s2 are switched.

Then, the controller issues an instruction to bit length adjuster 5701to generate an adjustment bit string, which is constructed with thePadNum bits to adjust the bit length (S5903).

For example, the adjustment bit string used to adjust the bit length maybe constructed with “0 (zero)” of the PadNum bits or “1” of the PadNumbits. It is only necessary that the information about the adjustment bitstring that is constructed with the PadNum bits to adjust the bit lengthbe shared by the transmitter including the modulator in FIG. 57 and thereceiver that receives the modulated signal transmitted from thetransmitter. Accordingly, it is necessary that the adjustment bit stringthat is constructed with the PadNum bits to adjust the bit length begenerated according to a specific rule, and that the specific rule beshared by the transmitter and the receiver. Accordingly, the adjustmentbit string, which is constructed with the PadNum bits to adjust the bitlength, is not limited to the above example.

First bit string 503 is input to bit length adjuster 5701, and bitlength adjuster 5701 adds the adjustment bit string (that is, theadjustment bit string that is constructed with the PadNum bits to adjustthe bit length) to a rear end or a leading end of the code word of theerror correction code having code word length (block length (codelength)) N, and outputs the second bit string for the mapper, the numberof bits constituting the second bit string being a multiple of thenumber of bits (X+Y).

Effect of First Exemplary Embodiment

When the encoder outputs the code word of the error correction codehaving code word length (block length (code length)) N, the number ofbits (X+Y) that can be transmitted at the identical frequency and theidentical time using first and second complex signals s1 and s2 does notinclude the data of the plurality of blocks (of the error correctioncode) irrespective of the value of N with respect to a set of complexsignals based on any combination of the modulation schemes. Therefore,there is a high possibility of reducing the memory of the transmitterand/or receiver.

Bit length adjuster 5701 may be included in one of functions of encoder502 or mapper 504.

Second Exemplary Embodiment

FIG. 60 illustrates a configuration of a modulator according to a secondexemplary embodiment.

The modulator of the second exemplary embodiment includes encoder 502LA,bit length adjuster 6001, and mapper 504. Because of the identicalprocessing of mapper 504, the description is omitted.

<Encoder502LA>

A K-bit (K is a natural number) information bit is input to encoder502LA, and encoder 502LA obtains and outputs the code word of the LDPCcode of the systematic code constructed with N bits (N is a naturalnumber), where N>K. It is assumed that a parity check matrix of the LDPCcode has an accumulate structure in order to obtain the bit string of an(N−K)-bit parity portion except for the information portion.

Information about an 0 block that is of input for LDPC coding isrepresented as X_(i,j) (i is an integer, and j is an integer from 1 toN). The parity obtained after the coding is represented as P_(i,k) (k isan integer from N+1 to K). A vector of the code word of the LDPC code inthe ith block is represented as u=(X₁,X₂,X₃, . . .,X_(K−2),X_(K−1),X_(K),P_(K+1),P_(K+2),P_(K+3), . . .,P_(N−2),P_(N−1),P_(N))^(T), and the parity check matrix of the LDPCcode is represented as H. Therefore, Hu=0 holds (in this case, “0 (zero)of Hu=0” means a vector in which all elements are 0).

At this point, parity check matrix H is illustrated in FIG. 61 . Asillustrated in FIG. 61 , in parity check matrix H, the number of rows is(N−K) (first to (N−K)th rows exist), and the number of columns is N(first to Nth columns exist). The number of rows of partial matrix(61-1) (Hcx) associated with the information is (N−K) (first to (N−K)throws exist), and the number of columns is K (first to Kth columnsexist). The number of rows of parity-associated partial matrix (61-2)(Hcp) is (N−K) (first to (N−K)th rows exist), and the number of columnsis (N−K) (first to (N−K)th columns exist). Therefore, parity checkmatrix H=[HcxHcp] is obtained.

FIG. 62 illustrates a configuration of parity-associated partial matrixHcp in LDPC-code parity check matrix H having the accumulate structurein the second exemplary embodiment. As illustrated in FIG. 62 , assumingthat H_(cp,comp)[i][j] (i and j are an integer from 1 to (N−K) (i andj=1, 2, 3, . . . , N−K−1, and N−K)) is an element of parity-associatedpartial matrix Hcp in the ith row and the ith column, the followingequation holds.

[Mathematical Formula 355]

For i=1H _(cp,comp)[1][1]=1  (1-1)H _(cp,comp)[1][j]=0 for ∀j; j=2,3, . . . ,N−K−1,N−K  (1-2)(j is an integer from 2 to (K−N) (j=2, 3, . . . , N−K−1, and N−K), andequation (1-2) holds in all values of j)

[Mathematical Formula 356]

For i≠1 (i is an integer from 2 to (N−K), namely, i=2, 3, . . . , N−K−1,and N−K):H _(cp,comp) [i][i]=1 for ∀i; i=2,3, . . . ,N−K−1,N−K  (2-1)(i is an integer from 2 to (N−K) (i=2, 3, . . . , N−K−1, and N−K), andequation (2-1) holds in all values of i)H _(cp,comp) [i][i−1]=1 for ∀i;i=2,3, . . . ,N−K−1,N−K  (2-2)(i is an integer from 2 to (N−K) (i=2, 3, . . . , N−K−1, and N−K), andequation (2-2) holds in all values of i)H _(cp,comp) [i][j]=0 for ∀i∀j; i≠j; i−1≠j; i−1≠j; i=2, 3, . . .,N−K−1,N−K; j=1, 2, 3, . . . ,N−K−1,N−K   (2-3)(i is an integer from 2 to (N−K) (i=2, 3, . . . , N−K−1, and N−K), j isan integer from 1 to (N−K) (j=1, 2, 3, . . . , N−K−1, and N−K), and {i≠jor i−1≠j}, and equation (2-3) holds in all the values of i and jsatisfying {i≠j or i−1≠j})

FIG. 63 is a flowchart illustrating LDPC coding processing performedwith encoder 502LA.

Encoder 502LA performs the calculation associated with the informationportion in the code word of the LDPC code. The jth (j is an integer from1 to (N−K)) row of parity check matrix H will be described by way ofexample.

The calculation is performed using the jth vector of partial matrix(61-1) (Hex) associated with the information about parity check matrix Hand information X_(i,j) about the ith block to obtain intermediate valueY_(i,j) (S6301).

Encoder 502LA performs the following calculation to obtain the paritybecause parity-associated partial matrix (61-2) (Hcp) has the accumulatestructure.P _(i,N+j) =Y _(i,j) EXOR P _(i,N+j−1)

(EXOR is an addition in which 2 is used as a modulus.) However, thefollowing calculation is performed for j=1.P _(i,N+1) =Y _(i,j) EXOR 0

FIG. 64 illustrates a configuration example performing the accumulateprocessing. In FIG. 64 , reference mark 64-1 designates exclusive OR,reference mark 64-2 designates a register, and an initial value ofregister 64-2 is “0 (zero)”.

<Bit Length Adjuster 6001>

Similarly to the bit length adjuster of the first exemplary embodiment,first bit string 503 that is of the N-bit code word (block length (codelength)) is input to bit length adjuster 6001, and bit length adjuster6001 adjusts the bit length to output second bit string 6003.

One of the characteristic points of the second exemplary embodiment isthat the bit value in a predetermined portion of the N-bit code word (ofthe ith block) obtained through the coding processing is repeatedly usedat least once (repetition).

FIG. 65 is a flowchart illustrating the bit length adjustment processingof the second exemplary embodiment.

The bit length adjustment processing is started on the conditioncorresponding to the start of step S5807 in FIG. 58 of the firstexemplary embodiment.

Flow many bits needs to be adjusted is decided similarly to FIG. 58(step S6501). The processing in step S6501 corresponds to step S5901 inFIG. 59 of the first exemplary embodiment.

Then, the controller issues an instruction to bit length adjuster 6001to repeat the bit value in the predetermined portion of the N-bit codeword to generate a bit string for adjustment (hereinafter, referred toas an “adjustment bit string”) (S6503).

An example of an adjustment bit string generating method will bedescribed below with reference to FIGS. 66, 67, and 68 .

As described above, the vector of the code word of the LDPC code in theith block is represented as u=(X₁,X₂,X₃, . . .,X_(K−2),X_(K−1),X_(K),P_(K+1),P_(K+2),P_(K+3), . . .,P_(N−2),P_(N−1),P_(N))^(T).

<“Adjustment Bit String” Generating Method of (Example 1) in FIG. 66 >

In (Example 1) of FIG. 66 , information X_(a) of the information bits isextracted from the vector of the code word of the LDPC code in the ithblock u=(X₁,X₂,X₃, . . . ,X_(K−2),X_(K−1),X_(K),P_(K+1),P_(K+2),P_(K+3),. . . ,P_(N−2),P_(N−1),P_(N))^(T) (66-1). Information X_(a) is repeatedto generate the plurality of reiteration bits, and Information X_(a) asthe plurality of reiteration bits are added to the code word of the LDPCcode of the ith block as adjustment bit string 66-2 (66-1 and 66-2 inFIG. 66 ). Accordingly, in bit length adjuster 6001 of FIG. 60 , firstbit string (503) that is of the input of bit length adjuster 6001 inFIG. 60 constitutes the code word of the LDPC code in the ith block, andsecond bit string (6003) that is of the output of bit length adjuster6001 in FIG. 60 constitutes code word 66-1 of the LDPC code in the ithblock and adjustment bit string 66-2.

In (Example 1) of FIG. 66 , the adjustment bit string is inserted in(added to) the tail end. Alternatively, the adjustment bit string may beinserted in any position of the code word of the LDPC code in the ithblock. Alternatively, the plurality of blocks constructed with at leastone bit may be generated from the adjustment bit string, and each blockmay be inserted in any position of the code word of the LDPC code in theith block.

<“Adjustment Bit String” Generating Method of (Example 2) in FIG. 66 >

In (Example 2) of FIG. 66 , bit P_(b) in the parity bit is extractedfrom the vector of the code word of the LDPC code in the ith blocku=(X₁, X₂, X₃, . . . , X_(K−2), X_(K−1), X_(K), P_(K+1), P_(K+2),P_(K+3), . . . , P_(N−2), P_(N−1), P_(N))^(T) (66-3). Bit P_(b) isrepeated to generate reiteration of the plurality of bits P_(b), and theplurality of bits P_(b) are added to the code word of the LDPC code ofthe ith block as adjustment bit string 66-2 (66-3 and 66-4 in FIG. 66 ).Accordingly, in bit length adjuster 6001 of FIG. 60 , first bit string(503) that is of the input of bit length adjuster 6001 in FIG. 60constitutes the code word of the LDPC code in the ith block, and secondbit string (6003) that is of the output of bit length adjuster 6001 inFIG. 60 constitutes code word 66-3 of the LDPC code in the ith block andadjustment bit string 66-4.

In (Example 2) of FIG. 66 , the adjustment bit string is inserted in(added to) the tail end. Alternatively, the adjustment bit string may beinserted in any position of the code word of the LDPC code in the ithblock. Alternatively, the plurality of blocks constructed with at leastone bit may be generated from the adjustment bit string, and each blockmay be inserted in any position of the code word of the LDPC code in theith block.

<“Adjustment Bit String” Generating Method in FIG. 67 >

In FIG. 67 , M bits of the vector of the code word of the LDPC code inthe ith block are selected from u=(X₁, X₂, X₃, . . . , X_(K−2), X_(K−1),X_(K), P_(K+1), P_(K+2), P_(K+3), . . . , P_(N−2), P_(N−1), P_(N))^(T)(67-1). For example, the selected bits include X_(a) and P_(b), and eachof the selected M bits is copied once. At this point, it is assumed thatvector m constructed with the M bits is represented as m=[X_(a), P_(b),. . . ]. Vector m=[X_(a), P_(b), . . . ] is added to the code word ofthe LDPC code of the ith block as adjustment bit string 67-2 (67-1 and67-2 in FIG. 67 ). Accordingly, in bit length adjuster 6001 of FIG. 60 ,first bit string (503) that is of the input of bit length adjuster 6001in FIG. 60 constitutes the code word of the LDPC code in the ith block,and second bit string (6003) that is of the output of bit lengthadjuster 6001 in FIG. 60 constitutes code word 67-1 of the LDPC code inthe ith block and adjustment bit string 67-2.

In FIG. 67 , the adjustment bit string is inserted in (added to) thetail end. Alternatively, the adjustment bit string may be inserted inany position of the code word of the LDPC code in the ith block.Alternatively, the plurality of blocks constructed with at least one bitmay be generated from the adjustment bit string, and each block may beinserted in any position of the code word of the LDPC code in the ithblock.

The adjustment bit string may be generated from only the informationbit, only the parity bit, or both the information bit and the paritybit.

<“Adjustment Bit String” Generating Method in FIG. 68 >

In FIG. 68 , M bits of the vector of the code word of the LDPC code inthe ith block are selected from u=(X₁, X₂, X₃, . . . , X_(K−2), X_(K−1),X_(K), P_(K+1), P_(K+2), P_(K+3), . . . , P_(N−2), P_(N−1), P_(N))^(T)(68-1). For example, the selected bits include X_(a) and P_(b), and eachof the selected M bits is copied once. At this point, it is assumed thatvector m constructed with the M bits is represented as m=[X_(a), P_(b),. . . ].

Each bit of vector m=[X_(a), P_(b), . . . ] constructed with M bits iscopied at least once, and vector γ constructed with T bits isrepresented as γ=[X_(a),X_(a), P_(b), . . . ] (M<Γ). Vector γ=[X_(a),X_(a), P_(b), . . . ] is set to the “adjustment bit string” (68-2), andthe “adjustment bit string” (68-2) is added to the code word of the LDPCcode of the ith block (68-1 and 68-2 in FIG. 68 ).

Accordingly, in bit length adjuster 6001 of FIG. 60 , first bit string(503) that is of the input of bit length adjuster 6001 in FIG. 60constitutes the code word of the LDPC code in the ith block, and secondbit string (6003) that is of the output of bit length adjuster 6001 inFIG. 60 constitutes code word 68-1 of the LDPC code in the ith block andadjustment bit string 68-2.

In FIG. 68 , the adjustment bit string is inserted in (added to) thetail end. Alternatively, the adjustment bit string may be inserted inany position of the code word of the LDPC code in the ith block.Alternatively, the plurality of blocks constructed with at least one bitmay be generated from the adjustment bit string, and each block may beinserted in any position of the code word of the LDPC code in the ithblock.

The adjustment bit string may be generated from only the informationbit, only the parity bit, or both the information bit and the paritybit.

<The Number of Adjustment Bit Strings Generated with Bit Length Adjuster6001>

The number of adjustment bit strings generated with bit length adjuster6001 can be decided similarly to the first exemplary embodiment. Thispoint will be described below with reference to FIG. 60 .

In FIG. 60 , first complex signal s1 (s1(t), s1 (f), or s1(t,f) (where tis the time and f is the frequency)) is a baseband signal that can beexpressed by in-phase component I and quadrature component Q based onthe mapping of a certain modulation scheme such as BPSK, QPSK, 16QAM,64QAM, and 256QAM. Similarly, second complex signal s2 (s2(t), s2(f), ors2(t,f)) is a baseband signal that can be expressed by in-phasecomponent I and quadrature component Q based on the mapping of a certainmodulation scheme such as BPSK, QPSK, 16QAM, 64QAM, and 256QAM.

The second bit string is input to mapper 504. (X+Y) bit strings areinput to mapper 504. Using a number of first bits X in the (X+Y) bitstrings, mapper 504 generates first complex signal s1 based on themapping of a first modulation scheme. Similarly, using a number ofsecond bits Y in the (X+Y) bit strings, mapper 504 generates secondcomplex signal s2 based on the mapping of a second modulation scheme.

Encoder 502 performs the coding (of the error correction code) from aK-bit information bit string, and outputs first bit string (503) that isof an N-bit code word.

Depending on the number of values (X+Y), sometimes the code word length(N bits) that is of the output of the encoder is not a multiple of thenumber of bits (X+Y) used to generate two complex signals s1 and s2.

For example, it is assumed that code word length N has 64800 bits, 64QAMis used as the modulation scheme, and X=6 holds, or 256QAM is used asthe modulation scheme and Y=8 and X+Y=14 hold. Alternatively, forexample, it is assumed that code word length N has 16200 bits, 256QAM isused as the modulation scheme, and X=8 holds, or 256QAM is used as themodulation scheme and Y=8 and X+Y=16 hold.

In both the cases, the code word length (N bits) that is of the outputof the encoder is not a multiple of the number of bits (X+Y) used togenerate two complex signals s1 and s2.

Therefore, in the second exemplary embodiment, even if the code wordoutput from the encoder has any length (N bits), bit length adjuster6001 performs the adjustment such that the mapper performs processingwithout leaving the number of bits.

An advantage of the case that the code word length (N bits) that is ofthe output of the encoder is a multiple of the number of bits (X+Y) usedto generate two complex signals s1 and s2 will be described assupplement.

A method in which the transmitter efficiently transmits one block of theerror correction code having the N-bit code word length used in thecoding is considered. There is a higher possibility of being able toreduce a memory of the transmitter and/or receiver, in the case wherethe number of bits (X+Y) transmitted by first and second complex signalss1 and s2 at the identical frequency and the identical time isconstructed with the bits of the plurality of blocks.

For (modulation scheme of first complex signal s1, modulation scheme ofsecond complex signal s2)=(16QAM,16QAM), the number of bits (X+Y) of 8bits can be transmitted by first and second complex signals s1 and s2 atthe identical frequency and the identical time, and the 8 bitspreferably do not include data of the plurality of blocks (of the errorcorrection code). That is, in the modulation scheme selected by thetransmitter, the number of bits (X+Y) transmitted by first and secondcomplex signals s1 and s2 at the identical frequency and the identicaltime preferably does not include data of the plurality of blocks (of theerror correction code).

Accordingly, the code word length (N bits) that is of the output of theencoder is preferably a multiple of the number of bits (X+Y) used togenerate two complex signals s1 and s2.

In the transmitter, there is a high possibility of being able to switchthe plurality of modulation schemes in both the modulation schemes offirst and second complex signals s1 and s2. Accordingly, the number ofbits (X+Y) has a high possibility of taking a plurality of values.

At this point, “the code word length (N bits) that is of the output ofthe encoder is a multiple of the number of bits (X+Y) used to generatetwo complex signals s1 and s2” is not always satisfied in all the valuesthat can be taken by the number of bits (X+Y). Accordingly, processingmethods of the following exemplary embodiments are required.

Mapper 504 selects the first modulation scheme that is of the modulationscheme used to generate complex signal s₁(t) and the second modulationscheme that is of the modulation scheme used to generate complex signals₂(t) according to control signal 512. First and second complex signalss₁(t) and s₂(t) are generated using the bit string of the number of bits(X+Y), which is obtained from the number of first bits X used togenerate first complex signal s1 and the number of second bits Y used togenerate second complex signal s2 in input second bit string 6003.

First bit string 503 is input to bit length adjuster 6001, and bitlength adjuster 6001 adjusts the bit length (in this case, the code wordlength (block length (code length)) of the code word (block) of theerror correction code) of first bit string 503 to generate second bitstring 5703.

FIG. 58 is a flowchart illustrating bit length adjustment processing ina modulation processing method of the second exemplary embodiment.

A controller (not illustrated) acquires the number of bits (X+Y) whichis obtained from the number of first bits X used to generate firstcomplex signal s1 and the number of second bits Y used to generatesecond complex signal s2 (step S5801).

The controller determines whether the code word length (block length(code length)) of the code word (block) of the error correction codeneeds to be adjusted (S5803). Whether N bits of the code word length(block length (code length)) of the error correction code are a multipleof the value of (X+Y) can be used as a criterion. Alternatively, thedetermination may be made using an association table between the valueof (X+Y) and the number of bits X. The information about (X+Y) may beinformation about the first modulation scheme that is of the modulationscheme used to generate complex signal s₁(t) and the second modulationscheme that is of the modulation scheme used to generate complex signals₂(t).

If the code word length (block length (code length)) N of the errorcorrection code is 64800 bits and the value of (X+Y) is 16, the codeword length N bits of the error correction code are a multiple of thevalue of (X+Y). The controller determines that the bit length does notneed to be adjusted (NO in S5803).

When determining that the necessity of the adjustment of the bit lengthis eliminated (NO in S5803), the controller sets bit length adjuster5701 such that bit length adjuster 5701 directly outputs input first bitstring 503 as second bit string 5703 (S5805). That is, in bit lengthadjuster 5701, the 64800-bit code word of the error correction codeserves as the input, and the 64800-bit code word of the error correctioncode serves as the output (bit length adjuster 5701 directly outputsinput bit string 503 to the mapper as second bit string 5703).

If the code word length (block length (code length)) N of the errorcorrection code is 64800 bits and the value of (X+Y) is 14, the codeword length N bits of the error correction code are not a multiple ofthe value of (X+Y). In this case, the controller determines that the bitlength needs to be adjusted (YES in S5803).

When determining that the bit length needs to be adjusted, thecontroller sets bit length adjuster 5701 such that bit length adjuster5701 performs bit length adjustment processing on input first bit string503 (S5805). That is, in the second exemplary embodiment, as describedabove, the adjustment bit string is generated through the bit lengthadjustment processing, and added to the vector of the code word of theLDPC code in the ith block (for example, see FIGS. 66, 67, and 68 ).

For example, in the case that the value of (X+Y), namely, the set of thefirst and second modulation schemes is switched (or in the case that thesetting of the set of the first and second modulation schemes can bechanged) while the vector of the code word of the LDPC code in the ithblock has fixed code word length (block length (code length)) N of 64800bits, the number of bits of the adjustment bit string is properlychanged (sometimes the necessity of the adjustment bit string iseliminated depending on the value of (X+Y) (the set of the first andsecond modulation schemes)).

One of the necessary points is that the code word of the LDPC code inthe ith block and the number of bits of second bit string (6003)constructed with the adjustment bit string are a multiple of the numberof bits (X+Y) decided by the set of the first and second modulationschemes.

An example of the characteristic adjustment bit string generating methodwill be described below.

FIGS. 69 and 70 illustrate a modification of the adjustment bit stringgenerated with the bit length adjuster. In FIGS. 69 and 70 , first bitstring 503 constitutes the input of bit length adjuster 6001 in FIG. 60. Bit length adjuster 6001 outputs second bit string 6003. In FIGS. 69and 70 , for convenience, second bit string 6003 has a configuration inwhich the adjustment bit string is added to the rear end of first bitstring 503 (however, the position to which the adjustment bit string isadded is not limited to the position in FIGS. 69 and 70 ).

<Legend>

Square frames indicate individual bits of first bit string 503 or secondbit string 6003.

In FIGS. 69 and 70 , a square frame surrounding “0” indicates a bithaving the value of “0”.

In FIGS. 69 and 70 , a square frame surrounding “1” indicates a bithaving the value of “1”.

In FIGS. 69 and 70 , p_last that is of a hatched square frame indicatesa value of the bit of the position corresponding to a final output bitof the accumulate processing. In the LDPC code in which theparity-associated partial matrix has the accumulate structure for theabove parity check matrix, p_last constitutes P_(N) in the case that thevector of the code word of the LDPC code in the ith block is set tou=(X₁, X₂, X₃, . . . , X_(K−2), X_(K−1), X_(K), P_(K+1), P_(K+2),P_(K+3), . . . , P_(N−2), P_(N−1), P_(N))^(T) (in the parity checkmatrix, p_last constitutes the bit associated with the final column ofthe partial matrix associated with the parity of the accumulatestructure in the LDPC code in which the parity-associated partial matrixhas the accumulate structure).

A blackened square frame (connected) indicates one of the bits that areused to derive the value of p_last when encoder 502 performs theprocessing in FIG. 63 .

One of the connected bits is the value of the bit corresponding tonext-to-last bit p_2ndlast used to derive p_last in accumulateprocessing of step S6303. In the case that the vector of the code wordof the LDPC code in the ith block is set to u=(X₁, X₂, X₃, . . . ,X_(K−2), X_(K−1), X_(K), P_(K+1), P_(K+2), P_(K+3), . . . , P_(N−2),P_(N−1),P_(N))^(T), the connected bit in p_2ndlast constitutes P_(N−1)in the LDPC code in which the parity-associated partial matrix has theaccumulate structure.

The vector constituting an (N−K)th row is set to h_(N−K) in parity checkmatrix H (a matrix having the order of (N−K) rows and N columns) inwhich the parity-associated partial matrix in which the vector of thecode word of the LDPC code in the ith block is set to u=(X₁, X₂, X₃, . .. , X_(K−2), X_(K−1), X_(K), P_(K+1), P_(K+2), P_(K+3), . . . , P_(N−2),P_(N−1), P_(N))^(T) has the accumulate structure. At this point, h_(N−K)is a vector having the order of one row and N columns.

In vector h_(N−K), a column that becomes “1” is set to g. g is aninteger from 1 to K. At this point, X_(g) also serves as a candidate asthe connected bit.

In FIGS. 69 and 70 , a square frame surrounding “any” is a bit of one of“0” and “1”.

A length of an arrow indicated by PadNum is the number of adjustmentbits in the case that the bit length is adjusted (by a method forsupplying a shortage).

An example will be described below. The hatched p_last constitutesP_(N).

Bit length adjuster 6001 in FIG. 60 generates one of the adjustment bitstrings of the following modifications (as described above, theadjustment bit string arranging method is not limited to that in FIG. 60).

First Modification in FIG. 69

Bit length adjuster 6001 generates the adjustment bit string byrepeating the value of p_last at least once.

Second Modification in FIG. 69

Bit length adjuster 6001 generates a part of the adjustment bit stringby repeating the value of p_last at least once. For “any”, the vector ofthe code word of the LDPC code in the ith block is generated from one ofbits of u=(X₁, X₂, X₃, . . . , X_(K−2), X_(K−1), X_(K), P_(K+1),P_(K+2), P_(K+3), . . . , P_(N−2), P_(N−1), P_(N))^(T).

Third Modification in FIG. 69

Bit length adjuster 6001 generates a part of the adjustment bit stringby repeating the value of p_last at least once. The part of theadjustment bit string is constructed with a predetermined bit.

Fourth Modification in FIG. 70

Bit length adjuster 6001 generates the adjustment bit string byrepeating the value of the connected bit at least once.

Fifth Modification in FIG. 70

Bit length adjuster 6001 generates a part of the adjustment bit stringby repeating the value of the connected bit at least once. For “any”,the vector of the code word of the LDPC code in the ith block isgenerated from one of bits of u=(X₁, X₂, X₃, . . . , X_(K−2), X_(K−1),X_(K), P_(K+1), P_(K+2), P_(K+3), . . . , P_(N−2), P_(N−1), P_(N))^(T).

Sixth Modification in FIG. 70

Bit length adjuster 6001 generates the adjustment bit string from thevalues of p_last and the connected bit.

Seventh Modification in FIG. 70

Bit length adjuster 6001 generates a part of the adjustment bit stringfrom the values of p_last and the connected bit. For “any”, the vectorof the code word of the LDPC code in the ith block is generated from oneof bits of u=(X₁, X₂, X₃, . . . , X_(K−2), X_(K−1), X_(K), P_(K+1),P_(K+2), P_(K+3), . . . , P_(N−2), P_(N−1), P_(N))^(T).

Eighth Modification in FIG. 70

Bit length adjuster 6001 generates a part of the adjustment bit stringfrom the values of p_last and the connected bit. The part of theadjustment bit string is constructed with a predetermined bit.

Ninth Modification in FIG. 70

Bit length adjuster 6001 generates a part of the adjustment bit stringfrom the value of the connected bit. The part of the adjustment bitstring is constructed with a predetermined bit.

Effect of Second Exemplary Embodiment

FIG. 71 is a view illustrating one of perceptions according to thedisclosure associated with the second exemplary embodiment.

An upper stage in FIG. 71 is a reproduction diagram illustrating thefirst bit string (the code word of the LDPC code in the ith block) 503in FIGS. 69 and 70 .

A middle stage in FIG. 71 is a conceptual view illustrating parity checkmatrix H of the LDPC code conceived through LDPC coding processingassociated with the accumulate processing (in step S6303).

“1” in FIG. 71 forms an edge when a Tanner graph is drawn in theconceptual parity check matrix of the LDPC code. As described in stepS6303, the value of p_last is calculated using the value of p_2ndlast.However, the value of p_last is a final bit in the order of theaccumulate processing, but does not have the association with the nextbit value. Accordingly, in conceptual parity check matrix H, a columnweight of p_last (or the bit corresponding to p_last) is less thancolumn weight 2 of the bit of another parity portion, and becomes columnweight 1 (as used herein, the column weight means a number having anelement of “1” in column vector of each column of the parity checkmatrix).

A lower stage in FIG. 71 illustrates a Tanner graph of conceptual paritycheck matrix H.

A round (◯) indicates a variable (bit) node. The hatched round indicatesa variable (bit) node giving an abstract of p_last. The blackened roundindicates a bit node giving an abstract of the connected bit. At thelower stage in FIG. 71 , a square (□) indicates a check node where thevariable (bit) nodes are coupled to each other. Particularly, the checknode indicated by checknode_last is one to which the bit node giving theabstract of p_last is connected (edge 1 is set). A solid line at thelower stage in FIG. 71 indicates a variable (bit) node havingchecknode_last and an edge.

The connected bit is a bit group that is directly connected tochecknode_last including p_2ndlast. At the lower stage in FIG. 71 , asold line indicates the edge that is directly connected to the bit nodeconnected to checknode_last. At the lower stage in FIG. 71 , a brokenline indicates the edge of conceptual parity check matrix FI of anothercheck node.

It is considered that BP (Belief Propagation) decoding such assum-product decoding is performed in the LDPC code in whichparity-associated partial matrix has the accumulate structure.

The Tanner graph at the lower stage in FIG. 71 is focused on.Particularly, the graph formed by the variable (bit) node and check nodeof the parity is focused on.

At this point, the variable (bit) node giving the abstract of the bit ofthe parity portion, such as p_2ndlast, which is different from p_last,is connected to two check nodes (the number of edges is 2 in FIG. 71 ).

With respect to the graph formed by the variable (bit) node and checknode of the parity, an external value can be obtained from (the checknodes of) two directions in the case that the number of parity edges is2. Because repetitive decoding is performed, belief propagates from thedistant check node and variable (bit) node.

On the other hand, with respect to the graph formed by the variable(bit) node and check node of the parity, the variable (bit) node givingthe abstract of p_last shares the edge only with one check node(checknode_last) (the line in which the number of edges is 1 in FIG. 71).

Therefore, the variable (bit) node of p_last means that the externalvalue is obtained only from one direction. The belief propagates fromthe distant check node and variable (bit) node because the repetitivedecoding is performed, and the external value is obtained only from onedirection in the variable (bit) node of p_last. Therefore, because manyreliabilities are hardly obtained, the belief of p_last is lower thanthe belief of another parity bit.

Accordingly, because of the low belief of p_last, an error propagationis generated to another bit.

When the belief of p_last is improved, the generation of an errorpropagation can be suppressed to improve the belief of another bit. Inthe second exemplary embodiment, this point is focused on and repetitivetransmission of p_last is proposed.

The bit in which the belief is lowered because of the low belief ofp_last is the connected bit (this point can be derived from the aboverelationship of “Hu=0”). Because of the low belief of the connected bit,the error propagation is generated to another bit.

Therefore, when the belief of the connected bit is improved, thegeneration of an error propagation can be suppressed to improve thebelief of another bit. In the second exemplary embodiment, this point isfocused on and repetitive transmission of the connected bit is proposed.

The plurality of exemplary embodiments may be combined.

Third Exemplary Embodiment

FIG. 73 illustrates a configuration of a modulator according to a thirdexemplary embodiment.

Referring to FIG. 73 , the modulator includes encoder 502LA, bitinterleaver 502BI, bit length adjuster 7301, and mapper 504.

Because the operation of mapper 504 is similar to that of the exemplaryembodiments, the description is omitted.

K-bit information about the ith block is input to encoder 502LA, andencoder 502LA outputs N-bit code word 503Λ of the ith block. At thispoint, it is assumed that N-bit bit string 5 has a specific number ofbits such as 4320 bits, 16800 bits, and 64800 bits.

For example, N-bit bit string 503Λ constituting the ith block is inputto bit interleaver 502BI, and bit interleaver 502BI performs bitinterleaving processing to output N-bit (interleaved) bit string 503V.In the interleaving processing, the order of the input bits of bitinterleaver 502BI is changed to output the bit string in which the orderis changed. For example, in the case that the column of the input bit ofthe bit interleaver 502BI has the column in which b1, b2, b3, b4, and b5are sequentially arranged, the output bit string of the bit interleaver502BI has the column in which b2, b4, b5, b1, and b3 through theinterleaving processing (however, there is not limited to the order).

For example, N-bit (bit-interleaved) bit string 503V is input to bitlength adjuster 7301, and bit length adjuster 7301 adjusts the bitlength, and outputs the bit-length-adjusted bit string 7303.

FIG. 74 is a view illustrating the operation of bit interleaver 502BI inFIG. 73 using the output bit string. FIG. 74 illustrates an example ofthe bit interleaving method, and another bit interleaving method may beadopted.

In FIG. 74 , a hatched square frame and a blackened square frame aresimilar to those in FIG. 69 of the second exemplary embodiment.

In FIG. 74 , reference mark 503Λ designates the order of the bit stringbefore the bit interleaving processing.

Reference mark 503U designates the order of the bit string after thefirst-time bit interleaving processing (σ1).

Reference mark 503V designates the order of the bit string after thesecond-time bit interleaving processing (σ2).

A solid-line arrow means that the bit at the position (order) of anarrow source moves to the position (order) of an arrow destinationthrough the first-time bit interleaving processing. For example, σ1(N−1) indicates a movement state of (Nth) p_last at a position of N−1that is of the final bit value of the parity portion through thefirst-time bit interleaving processing. In the example of FIG. 74 , σ1(N−1) is N−1 in which the position is not changed. σ1 (N−2) indicatesthe movement state of the position of p_2ndlast.

The bit interleaver is processing in which robustness against a bursterror in a communication path is strengthened by lengthening a distancebetween two adjacent bit positions in the code word generated by thecoding of the LDPC code, particularly the parity. Between p_last andp_2ndlast adjacent to each other in 503Λ immediately after the codingprocessing, a position space indicated by 503U is generated throughinterleaving processing σ1.

A broken-line arrow means that the bit at the position (order) of thearrow source moves to the position (order) of the arrow destinationthrough pieces of bit interleaving processing (σ1, σ2, . . . ). σ(N−1)is multiple syntheses and substitutions for σ1 and σ2. In the example ofFIG. 74 in which two substitutions are used, σ(N−1) is equivalent toσ2(σ1(N−1)).

Thus, bit interleaver 502BI is the processing in which the order of theinput bits of bit interleaver 502BI is changed to output the bit stringin which the order is changed.

FIG. 75 illustrates an example of mounting bit interleaver 502.

The bit string of an interleaving object is stored in a memory having asize of Nr and No that are of a divisor of the number of bits of the bitstring, and the write order of the bit string in the memory and the readorder are changed, thereby performing the bit interleaving processing.

First, the bit interleaver ensures the memory of the number of bits N ofthe bit interleaving processing object, where N=Nr×Nc.

Nr and No can be changed according to a coding rate of an errorcorrection code and/or the set modulation scheme (or the set of themodulation schemes).

In FIG. 75 , each of (Nr×Nc) squares indicates a storage in which thevalue of the corresponding bit is written (the value of 0 or 1 isaccumulated).

A longitudinally-repeated solid-line arrow (WRITE direction) means thatthe bit string is written in the memory from arrow source toward thearrow destination. In FIG. 75 , Bitfirst indicates the position wherethe initial bit is written. In each column, the leading write positionmay be changed.

A crosswise-repeated broken-line arrow (READ direction) indicates a readdirection.

The example in FIG. 75 illustrates the processing of rearranging the bitstring of the parity portion in 503Λ (what is called parity interleavingprocessing). The space between p_2ndlast and p_last, which are writtenin the memories in which addresses are continuous in the WRITEdirection, is increased.

FIG. 76 illustrates the bit length adjustment processing of the thirdexemplary embodiment.

The controller (not illustrated in FIG. 73 ) decides how many bits needsto be adjusted (step S7601). The processing in step S7601 corresponds tostep S5901 of the first exemplary embodiment.

Then the controller issues an instruction to bit length adjuster 7301 inFIG. 73 to assign the position where the bit string (for example, theadded bit described in the first exemplary embodiment and the adjustmentbit string described in the second exemplary embodiment) is added to theN-bit code word in the ith block after the bit interleaving (S7603).

An example will be described below with reference to FIG. 77 . In FIG.77 , reference mark 503V designates the interleaved bit string in FIG.73 . For example, interleaved bit string 503V is the interleaved N-bitcode word in the ith block. Reference mark 7303 designates thebit-length-adjusted bit string in FIG. 73 . In bit-length-adjusted bitstring 7303, it is assumed that the added bit string is added to theinterleaved N-bit code word in the ith block.

In FIG. 77 , a square frame (□) indicates each bit of the interleavedN-bit code word in the ith block, and a blackened square frame (▪)indicates the bit of the added bit string.

In the example of FIG. 77 , bit (▪) 7314 #1 of the added bit string isinserted between square frames (□) 7314 #1A and 7314 #1B, and bit (▪)7314 #2 of the added bit string is inserted between square frames (□)7314 #2A and 7314 #2B, thereby forming bit-length-adjusted bit string7303. That is, the added bit string is inserted in and added to theinterleaved N-bit code word in the ith block to generatebit-length-adjusted bit string 7303 (S7605).

As described above in the first and second exemplary embodiments, in thecase that the value of (X+Y), namely, the set of the first and secondmodulation schemes of s1 (t) and s2(t) is switched (or in the case thatthe setting of the set of the first and second modulation schemes ofs1(t) and s2(t) can be changed) while the vector of the code word (ofthe LDPC code) in the ith block has fixed code word length (block length(code length)) N of 64800 bits, the number of bits of the added bitstring is properly changed (sometimes the necessity of the added bitstring is eliminated depending on the value of (X+Y) (the set of thefirst and second modulation schemes of s1(t) and s2(t))).

One of the necessary points is that the number of bits ofbit-length-adjusted bit string (7303) constructed with the code word ofthe LDPC code in the ith block and the added bit string is a multiple ofthe number of bits (X+Y) decided by the set of the first and secondmodulation schemes of s1(t) and s2(t).

As described above, for example, N-bit (bit-interleaved) bit string 503Vis input to bit length adjuster 7301, and bit length adjuster 7301adjusts the bit length, and outputs the bit-length-adjusted bit string7303. Alternatively, for example, (N×z)-bit (bit-interleaved) bit string503V may be input to bit length adjuster 7301, and bit length adjuster7301 may adjust the bit length, and output bit-length-adjusted bitstring 7303 (z is an integer of 1 or more).

FIG. 75 illustrates an example of mounting bit interleaver 502.

The bit string of an interleaving object is stored in a memory having asize of Nr and Nc that are of a divisor of the number of bits of the bitstring, and the write order of the bit string in the memory and the readorder are changed, thereby performing the bit interleaving processing.

First, the bit interleaver ensures the memory of the number of bits(N×z) of the bit interleaving processing object, where N×z=Nr×Nc.

Nr and Nc can be changed according to a coding rate of an errorcorrection code and/or the set modulation scheme (or the set of themodulation schemes).

In FIG. 75 , each of (Nr×Nc) squares indicates a storage in which thevalue of the corresponding bit is written (the value of 0 or 1 isaccumulated).

A longitudinally-repeated solid-line arrow (WRITE direction) means thatthe bit string is written in the memory from the arrow source toward thearrow destination. In FIG. 75 , Bitfirst indicates the position wherethe initial bit is written. In each column, the leading write positionmay be changed.

A crosswise-repeated broken-line arrow (READ direction) indicates a readdirection.

The example in FIG. 75 illustrates the processing of rearranging the bitstring of the parity portion in 503Λ (what is called parity interleavingprocessing). The space between p_2ndlast and p_last, which are writtenin the memories in which addresses are continuous in the WRITEdirection, is increased.

FIG. 76 illustrates the bit length adjustment processing of the thirdexemplary embodiment.

The controller (not illustrated in FIG. 73 ) decides how many bits needsto be adjusted (step S7601). The processing in step S7601 corresponds tostep S5901 of the first exemplary embodiment.

Then the controller issues an instruction to bit length adjuster 7301 inFIG. 73 to assign the position where the bit string (for example, theadded bit described in the first exemplary embodiment and the adjustmentbit string described in the second exemplary embodiment) is added to zblocks each of which is constructed with the N-bit code word after thebit interleaving (S7603).

An example will be described below with reference to FIG. 77 . In FIG.77 , reference mark 503V designates the interleaved bit string in FIG.73 . For example, interleaved bit string 503V is the z blocks each ofwhich is constructed with the interleaved N-bit code word.

Reference mark 7303 designates the bit-length-adjusted bit string inFIG. 73 . In bit-length-adjusted bit string 7303, it is assumed that theadded bit string is added to the z blocks each of which is constructedwith the interleaved N-bit code word.

In FIG. 77 , a square frame (□) indicates each bit of the z blocks eachof which is constructed with the N-bit code word, and a blackened squareframe (▪) indicates the bit of the added bit string.

In the example of FIG. 77 , bit (▪) 7314 #1 of the added bit string isinserted between square frames (□) 7314 #1A and 7314 #1B, and bit (▪)7314 #2 of the added bit string is inserted between square frames (□)7314 #2A and 7314 #2B, thereby forming bit-length-adjusted bit string7303. That is, the added bit string is inserted in and added to the zblocks each of which is constructed with the interleaved N-bit code wordto generate bit-length-adjusted bit string 7303 (S7605).

Similarly to the first and second exemplary embodiments, in the casethat the value of (X+Y), namely, the set of the first and secondmodulation schemes of s1(t) and s2(t) is switched (or in the case thatthe setting of the set of the first and second modulation schemes of s1(t) and s2(t) can be changed) while the vector of the code word (of theLDPC code) in the ith block has fixed code word length (block length(code length)) N of 64800 bits, the number of bits of the added bitstring is properly changed (sometimes the necessity of the added bitstring is eliminated depending on the value of (X+Y) (the set of thefirst and second modulation schemes of s1(t) and s2(t))).

One of the necessary points is that the number of bits ofbit-length-adjusted bit string (7303) constructed with “the bit stringsof the z code words of the LDPC code in the ith block, namely, the(N×z)-bit bit string” and “the added bit string” is a multiple of thenumber of bits (X+Y) decided by the set of the first and secondmodulation schemes of s1(t) and s2(t).

Viewpoint of Third Exemplary Embodiment

(1) Measures against change of modulation scheme

As described in the first and second exemplary embodiments, one ofissues of the present disclosure is that measures are taken against thelack of bit in switching the set of the modulation schemes of complexsignals s1 (t) and s2(t).

(For Interleaving Size of N Bits)

(Effect 1)

As described above, the number of bits of bit-length-adjusted bit string(7303) constructed with the code word of the LDPC code in the ith blockand the added bit string is the multiple of the number of bits (X+Y)decided by the set of the first and second modulation schemes of s1(t)and s2(t).

Therefore, when the encoder outputs the code word of the errorcorrection code having the N-bit code word length (block length (codelength)), the number of bits (X+Y) that can be transmitted at theidentical frequency and the identical time using first and secondcomplex signals s1 and s2 does not include the data of the plurality ofblocks (of the error correction code) irrespective of the value of Nwith respect to a set of complex signals based on any combination of themodulation schemes. Therefore, there is a high possibility of reducingthe memory of the transmitter and/or receiver.

(Effect 2)

In the case that the value of (X+Y), namely, the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t) isswitched (or in the case that the setting of the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t)can be changed), bit length adjuster 7301 is disposed at the stagesubsequent to bit interleaver 502BI as illustrated in FIG. 73 , whichallows the memory size of the bit interleaver to be kept constantirrespective of the set of the first modulation schemes of s1(t) and thesecond modulation scheme of s2(t). Therefore, the increase in memorysize of the bit interleaver can be prevented. (When the order of bitlength adjuster 7301 and bit interleaver 502BI becomes reversed, it isnecessary to change the memory size due to the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t).For this reason, it is necessary to dispose bit length adjuster 7301 atthe stage subsequent to bit interleaver 502BI. In FIG. 73 , bit lengthadjuster 7301 is disposed just behind bit interleaver 502BI.Alternatively, an interleaver that performs another piece ofinterleaving or another processor may be inserted between bitinterleaver 502BI and bit length adjuster 7301.

A plurality of code word lengths (block lengths (code lengths)) of theerror correction code may be prepared. For example, it is assumed thatNa bits and Nb bits are prepared as the code word length (block length(code length)) of the error correction code. When the error correctioncode of the Na-bit code word length (block length (code length)) isused, the memory size of the bit interleaver is set to the Na bits, thebit interleaving is performed, and bit length adjuster 7301 in FIG. 73adds the added bit string as needed. Similarly, when the errorcorrection code of the Nb-bit code word length (block length (codelength)) is used, the memory size of the bit interleaver is set to theNb bits, the bit interleaving is performed, and bit length adjuster 7301in FIG. 73 adds the added bit string as needed.

(For (N×z)-bit interleaving)

(Effect 3)

As described above, the number of bits of bit-length-adjusted bit string(7303) constructed with “the bit strings of the z code words of the LDPCcode in the ith block, namely, the (N×z)-bit bit string” and “the addedbit string” is the multiple of the number of bits (X+Y) decided by theset of the first and second modulation schemes of s1 (t) and s2(t).

Therefore, when the encoder outputs the code word of the errorcorrection code having the N-bit code word length (block length (codelength)), the number of bits (X+Y) that can be transmitted at theidentical frequency and the identical time using first and secondcomplex signals s1 and s2 does not include the data of the plurality ofblocks except for the z code words irrespective of the value of N withrespect to a set of complex signals based on any combination of themodulation schemes. Therefore, there is a high possibility of reducingthe memory of the transmitter and/or receiver.

(Effect 4)

In the case that the value of (X+Y), namely, the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t) isswitched (or in the case that the setting of the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t)can be changed), bit length adjuster 7301 is disposed at the stagesubsequent to bit interleaver 502BI as illustrated in FIG. 73 , whichallows the memory size of the bit interleaver to be kept constantirrespective of the set of the first modulation schemes of s1(t) and thesecond modulation scheme of s2(t). Therefore, the increase in memorysize of the bit interleaver can be prevented. (When the order of bitlength adjuster 7301 and bit interleaver 502BI becomes reversed, it isnecessary to change the memory size due to the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t).For this reason, it is necessary to dispose bit length adjuster 7301 atthe stage subsequent to bit interleaver 502BI. In FIG. 73 , bit lengthadjuster 7301 is disposed just behind bit interleaver 502BI.Alternatively, an interleaver that performs another piece ofinterleaving or another processor may be inserted between bitinterleaver 502BI and bit length adjuster 7301.

A plurality of code word lengths (block lengths (code lengths)) of theerror correction code may be prepared. For example, it is assumed thatNa bits and Nb bits are prepared as the code word length (block length(code length)) of the error correction code. When the error correctioncode of the Na-bit code word length (block length (code length)) isused, the memory size of the bit interleaver is set to the (Na×z) bits,the bit interleaving is performed, and bit length adjuster 7301 in FIG.73 adds the added bit string as needed. Similarly, when the errorcorrection code of the Nb-bit code word length (block length (codelength)) is used, the memory size of the bit interleaver is set to the(Nb×z) bits, the bit interleaving is performed, and bit length adjuster7301 in FIG. 73 adds the added bit string as needed.

A plurality of bit interleaving sizes may be prepared with respect tothe code length (block length (code length)) of each error correctioncode. For example, when the error correction code has the N-bit codeword length, (N×a) bits and (N×b) bits are prepared as the bitinterleaving size (a and b are an integer of 1 or more). When the (N×a)bits are used as the bit interleaving size, the bit interleaving isperformed, and bit length adjuster 7301 in FIG. 73 adds the added bitstring as needed. Similarly, when the (N×b) bits are used as the bitinterleaving size, the bit interleaving is performed, and bit lengthadjuster 7301 in FIG. 73 adds the added bit string as needed.

Supplement of Third Exemplary Embodiment

(Method 1) Measures Against Change in Code Word Length N of ErrorCorrection Code

Code word length N of the error correction code is decided to be a valueincluding factor (X+Y), thereby obtaining a basic solution.

However, there is a limit in making code word length N of the errorcorrection code have a number constructed with factor (X+Y) in anypattern of the new set of the modulation schemes. For example, in orderto deal with the case of X+Y=6+8=14, it is necessary to set code wordlength N of the error correction code to a number that includes 7 as thefactor. Then, in order to deal with the case that a total value of 22 ofX=10 and Y=12 as the set of the modulation schemes, it is necessary toset code word length N of the error correction code to a new number alsoincluding the factor of 11.

(Method 2) Backward Compatibility with (Nr×Nc) Memory of Past BitInterleaver

As illustrated in FIG. 75 , some of the bit interleavers are constructedusing a difference between a write address and a read address of apredetermined number of (Nr×Nc) memories with respect to a predeterminednumber of bits. In a specification (standard) at a first stage, forexample, when the selectable modulation scheme becomes a number in which(X+Y) is less than or equal to 12, it is assumed that the bitinterleaving processing is properly performed on code word N of theerror correction code. In a specification (standard) at a second stage,for example, it is assumed that a new number of 14 is added as (X+Y).For X+Y=14, it is difficult to perform the control including the properbit interleaving in the specification (standard) at the first stage.This point will be described below with “the bit of which value shouldbe repeated” as p_last.

In FIG. 78 , the bit string adjuster is inserted at the front stage (notthe rear stage) of bit interleaver 502BI. A broken-line square frameindicates the tentatively-inserted bit length adjuster.

When the bit string adjuster is inserted at the front stage (not therear stage) of bit interleaver 502BI, the bit position of p_last is thefinal bit of bit string 503Λ.

In this case, second bit string 6003 in which the 6-bit adjustment bitis added to N-bit bit string 503 is output to the subsequent stage. Itis necessary for the interleaver that receives the 6-bit adjustment bitto perform the interleaving processing on the bit string having a newfactor (for example, 7 or 11) that is not a multiple of the (Nr×Nc) bitsdefined by the specification (standard) at the first stage. Accordingly,in the case that the bit string adjuster is inserted in the front stage(not the rear stage) of bit interleaver 502BI, there is a low affinityto the bit interleaver in the specification (standard) at the firststage.

On the other hand, in the configuration of the third exemplaryembodiment in FIG. 73 , bit length adjuster 7301 is located at the rearstage (not the front stage) of bit interleaver 502BI.

In the configuration, the N-bit code word of the error correction codein the specification (standard) at the first stage is input to bitinterleaver 502BI, and bit interleaver 502BI can perform the bitinterleaving processing suitable for the predetermined number of bits incode word length or code word 503.

Similarly to other exemplary embodiments, measures can be taken againstthe lack of bit corresponding to the number of bits (X+Y) used togenerate the set of complex signals s1(t) and s2(t).

Another Example

FIG. 79 illustrates a modulator according to a modification of the thirdexemplary embodiment.

The modulator includes bit value holder 7301A and adjustment bit stringgenerator 7301B, which constitute bit length adjuster 7301, at the rearstage of encoder 502LA.

Bit value holder 7301A directly supplies input N-bit bit string 503 tobit interleaver 502BI. Then, bit interleaver 502BI performs the bitinterleaving processing on bit string 503 having the N-bit bit length(the code length of the error correction code), and output bit string503V.

Bit value holder 7301A holds the bit value of “the bit position wherethe value should be repeated” in first bit string 503 output from theencoder, and supplies the bit value to adjustment bit string generator7301B.

Adjustment bit string generator 7301B generates one of the adjustmentbit strings of the second exemplary embodiment using the acquired “bitposition where the value should be repeated”, and outputs the adjustmentbit string included in first bit string 503 together with N-bit bitstring 503V.

In the modification, (1) the position of “the bit of which value shouldbe repeated” can easily be obtained without being influenced by the bitinterleaving pattern that is changed according to the coding rate of theerror correction code. For example, in the case that “the bit of whichvalue should be repeated” is p_last, the position of p_last can easilybe acquired. Therefore, the bit length adjuster can generate the bitstring from the reiteration of the finally-input bit that is of thefixed position.

(2) The modulator of the modification is suitable from the viewpoint ofthe affinity to the processing of the bit interleaver that is designedfor a predetermined code word length of the error correction code.

As indicated by the broken-line frame in FIG. 79 , the functions of bitvalue holder 7301A and adjustment bit string generator 7301B may beincluded in the function of bit interleaver 502BI.

Fourth Exemplary Embodiment

In the first to third exemplary embodiments, the shortage (PadNum bits)of the bit length of bit string 503 to the multiple of the value of(X+Y) is supplied by the adjustment bit string.

A method in which the excess bit length is shortened so as to be amultiple of the value of (X+Y) will be described in a fourth exemplaryembodiment. In the method of the fourth exemplary embodiment,particularly, known information is inserted at the front stage of thecoding of the error correction code, and the coding is performed on theinformation including the known information, and the known informationis deleted to adjust a bit series length. TmpPadNum is the number ofbits of the inserted known information, and is also the number of bitsdeleted after that.

FIG. 80 illustrates a configuration of a modulator of the fourthexemplary embodiment.

Bit length adjuster 8001 of the fourth exemplary embodiment includespreceding stage section 8001A and bit length adjuster subsequent stagesection 8001B.

Preceding stage section 8001A performs processing associated with thepreceding stage section. The preceding stage section temporarily addsthe adjustment bit string that is of the known information to the bitstring of the input information, and output the K-bit bit string.

The information bit string including the K-bit known information isinput to encoder 502, and encoder 502 outputs first bit string (503)that is of the coded N-bit code word. It is assumed that the errorcorrection code used in encoder 502 is a systematic code (the codeconstructed with the information and the parity).

Subsequent stage section 8001B performs processing associated with thesubsequent stage section. Bit string 503 is input to subsequent stagesection, and subsequent stage section deletes (removes) the adjustmentbit string that is of the known information temporarily inserted withpreceding stage section 8001A. Therefore, a series length ofbit-length-adjusted bit string 8003 output from preceding stage section8001A is a multiple of the value of (X+Y).

The value of (X+Y) is similar to that of the first to third exemplaryembodiments.

FIG. 81 is a flowchart illustrating processing of the fourth exemplaryembodiment.

Broken-line frame OUTER indicates the processing associated with thepreceding stage section.

The processing associated with the preceding stage section is processingin which the controller sets a processing content to the preceding stagesection. The controller (not illustrated in FIG. 80 ) outputs signalline 512.

The controller acquires bit length TmpPadNum of the known information inthe k-bit information of the N-bit code word of the error correctioncode based on the value of (X+Y) (S8101).

For example, the following calculation expression is considered as theacquired value.TmpPadNum=N−(floor(N/(X+Y))×(X+Y))

In the expression, floor is a function that rounds up figures after thedecimal point.

The value is not necessarily acquired by the calculation, but may beacquired using a table having a parameter such as code word length(block length) N of the error correction code of encoder 502.

Then the controller ensures a field of length TmpPadNum such that outputbit string 501 of the preceding stage section becomes K bits. That is,the controller performs control such that the information in K bits isK-TmpPadNum (bits) while the inserted known information is TmpPadNum(bits) (S8103).

(Example 1) In the case that preceding stage section 8001A in FIG. 80 isa part of a frame generating processor:

Preceding stage section 8001A in FIG. 80 may be located in a frameconfigurator that is a functionally front stage of the modulator.

For example, in a system such as DVB, a field having length TmpPadNummay previously be ensured in a baseband frame (what is called BB FRAME)configured usually as the K-bit (information) bit string according tothe value of (X+Y). FIG. 82 is a view illustrating a relationshipbetween BB FRAME having a length of K bits and an ensured length ofTmpPadNum. BB HEADER is a header of BB FRAME. DATA FIELD is a data bitstring having length DFL (bits). A first padding length that is of alength of the hatched portion is padding used to adjust the number ofbits that are an integral multiple of a TS packet and are less than DFLirrespective of the value of (X+Y). As illustrated in FIG. 82 , bitlength TmpPadNum that is of a temporarily padded number is ensured inaddition to the first padding.

The preceding stage section located at the input stage may ensure thefield length based on code word length N (including an index (such asthe coding rate) of a table providing information equivalent to codeword length N).

(Example 2) The case that preceding stage section 8001A in FIG. 80 isanother encoder that performs external code coding processing:

Preceding stage section 8001A in FIG. 80 may be an external codeprocessor that generates an external code coupled as the external codeof the code word of encoder 502 in the modulator.

In this case, the field for (X+Y) can be ensured by changing the codingrate (code word length) of the external code. For example, in the casethat a BCH code is used in the external code processing, code wordlength Nouter (of the external code) can be shortened by (X+Y) bydecreasing a degree of generator polynomial g(x) by (X+Y). The (X+Y)-bitfield can be ensured by this method.

There are various modifications in changing the degree. For example, avalue (or an index changing the degree) is set in a table such that thedegree of generator polynomial g(x) is smaller than that of the casethat no adjustment is required, and generator polynomial g(x) may beprovided through a control signal by the table.

The field means a field including at least one value of TmpPadNum thatis added or intermittently inserted irrespective of continuation ordiscretion of the bit arrangement in the K-bit bit string processed bythe code at the subsequent stage.

The controller issues an instruction to fill the field havinglengthTmpPadNum ensured in the preceding stage section with theadjustment bit string (known information) (S8105). Preceding stagesection 8001A in FIG. 80 fills the field with the adjustment bit string,and outputs bit string 501 having the K-bit length to encoder 502(S8105).

At this point, for example, it is assumed that all the values are 0(zero) in the known information (adjustment bit string). Encoder 502 inFIG. 80 codes the K bits constructed with the known information and thetransmission information, and obtains N-bit code word constructed withthe information and the parity (S8107). There is a method for settingall the values of the known information (adjustment bit string) to 0(zero) as one of methods for simply performing the coding. However, theknown information is not limited to one in which all the values are 0(zero) as long as what is the known information series can be shared bythe coding side and the decoding side. Bit interleaving processing maybe included in a processing result of encoder 502 in FIG. 80 .

Subsequent stage section 8001B in FIG. 80 removes thetemporarily-inserted adjustment bit string (known information) (or aninterleaved bit group corresponding to each bit of the originaladjustment bit string), and outputs second bit string(bit-length-adjusted bit string) 8003 having the number of bits shortenthan N bits (S8109). Subsequent stage section 8001B may be instructed toperform the processing in step S8109 by a value of a table thatindicates a position to be deleted according to the value of (X+Y).

Effect

In second bit string (bit-length-adjusted bit string) 8003 having(N−TmpPadNum) bits in which the temporarily-inserted adjustment bitstring is deleted from code length N of the code word of the LDPC codein the ith block, the number of bits (N−TmpPadNum) of second bit string(bit-length-adjusted bit string) 8003 is a multiple of the number ofbits (X+Y) decided by the set of the first modulation scheme of s1(t)and the second modulation scheme of s2(t).

In the case that the value of (X+Y), namely, the set of the first andsecond modulation schemes of s1(t) and s2(t) is switched (or in the casethat the setting of the set of the first and second modulation schemesof s1(t) and s2(t) can be changed) while the vector of the code word (ofthe LDPC code) in the ith block has fixed code word length (block length(code length)) N of 64800 bits, the number of adjustment bit strings(the number of bits TmpPadNum), which are temporarily inserted and thendeleted, is properly changed (sometimes the number of bits TmpPadNum iszero depending on the value of (X+Y) (the set of the first and secondmodulation schemes of s1 (t) and s2(t))).

Therefore, when the encoder outputs the code word of the errorcorrection code having the N-bit code word length (block length (codelength)), the number of bits (X+Y) that can be transmitted at theidentical frequency and the identical time using first and secondcomplex signals s1 and s2 does not include the data of the plurality ofblocks (of the error correction code) irrespective of the value of Nwith respect to a set of complex signals based on any combination of themodulation schemes. Therefore, there is a high possibility of reducingthe memory of the transmitter and/or receiver.

FIG. 83 illustrates a configuration of a modulator different from thatin FIG. 80 . In FIG. 83 , the component similar to that in FIG. 80 isdesignated by the identical reference mark. The modulator in FIG. 83differs from the modulator in FIG. 80 in that bit interleaver 502BI isinserted at the subsequent stage of encoder 502 and a preceding stage ofsubsequent stage section 8001B. The action of the modulator in FIG. 83will be described with reference to FIG. 84 .

FIG. 84 is a view illustrating the bit lengths of bit strings 501 to8003.

Bit string 501 is output from preceding stage section 8001A, and is the(information) bit string having the length of K bits including the fieldhaving length of TmpPadNum (bits) for the known information.

Bit string 503Λ is output from encoder 502, and is the bit string (firstbit string) having the length of N bits that are of the code word of theerror correction code.

Bit string 503V has the N-bit length in which the order of the bit valueis replaced by a bit interleaver.

Bit string 8003 is the second bit string (bit-length-adjusted bitstring) adjusted to the length of the (N−TmpPadNum) bits, and bit string8003 is output from subsequent stage section 8001B. Bit string 8003becomes one in which the known information having the TmpPadNum bits isdeleted from bit string 503V.

Effect of Fourth Exemplary Embodiment

In the configuration of the fourth exemplary embodiment, the code wordof the error correction code can be estimated (decoding) withoutperforming special processing in the decoding on the reception side.

In the configuration on the transmission side, the inserted adjustmentbit string is set to the known information, and only thetemporarily-inserted adjustment bit string (known information) isdeleted. Therefore, in the decoding of the receiver, a possibility ofobtaining a high error correction ability is enhanced because the errorcorrection code is decoded using the known information.

In the case that the processor performs the processing of generating theBCH or RS external code, suitably the field is easily ensured.

Fifth Exemplary Embodiment

A method and a configuration in which bit string 501 transmitted fromthe transmitter is decoded (on the receiver side) will be described infifth and sixth exemplary embodiments.

More particularly, modulation (detection) processing is performed oncomplex signals s1(t) and s2(t), which are generated from (information)bit string 501 by “the section that generates the modulated signal”(modulator) of the first to fourth exemplary embodiments and transmittedafter the pieces of processing such as MIMO pre-coding, and the bitstring is restored from complex signals (x1(t) and x2(t)).

Complex signals x1(t) and x2(t) are a complex baseband signal obtainedfrom the received signal received each receiving antenna.

FIG. 85 illustrates a bit string decoder of the receiver that receivesthe modulated signal transmitted by the transmission methods of thefirst to third exemplary embodiments.

In FIG. 85 , “{circumflex over ( )}” (caret) indicates an estimationresult of the signal having the reference mark under the caret,hereinafter, the caret is omitted by adding “{circumflex over ( )}” tothe reference mark.

The bit string decoder in FIG. 85 includes a detector (demodulator), abit length adjuster, and an error correction decoder.

The detector (demodulator) generates pieces of data, such as a harddecision value, a soft decision value, a log-likelihood and alog-likelihood ratio, which correspond to the bit of the number of bits(X+Y) of the number of first bits included in first complex signal s1and the number of second bits included in second complex signal s2, fromcomplex baseband signals x1(t) and x2(t) obtained from the receivedsignals received with the receiving antennas, and outputs the datastring corresponding to the second bit string having the length of anintegral multiple of (X+Y). For example, data strings {circumflex over( )}5703 corresponds to second bit string R202 having length (N+PadNum).

Data string {circumflex over ( )}5703 corresponding to the bit string ofthe second bit string is input to the bit length adjuster in FIG. 85 .The bit length adjuster extracts data corresponding to the adjustmentbit string having length PadNum inserted on the transmission side, andoutputs the data to the error correction decode, or outputs data string({circumflex over ( )}503V) corresponding to N bit strings.

The deinterleaver deinterleaves data string ({circumflex over ( )}503V)corresponding to the N bit strings, and outputs N deinterleaved datastrings ({circumflex over ( )}503Λ) to the error correction decoder.Data strings {circumflex over ( )}503V and {circumflex over ( )}503Λcorrespond to bit strings 503V and 503Λ, respectively.

The data corresponding to the adjustment bit string having length PadNumand N deinterleaved data strings ({circumflex over ( )}503Λ) are inputto the error correction decoder in FIG. 85 , and the error correctiondecoder performs error correction decoding (for example, BP (BeliefPropagation) decoding (such as sum-product decoding, min-sum decoding,Normalized BP decoding and offset BP decoding) or Bit Flipping decodingfor the use of the LDPC code) to obtain a K-bit information bitestimation series.

In the case that the bit interleaver is used on the transmission side, adeinterleaver is inserted as illustrated in FIG. 85 . On the other hand,in the case that the bit interleaver is used on the transmission side,the necessity of the deinterleaver in FIG. 85 is eliminated.

FIG. 86 is a view illustrating the input and output of the bit stringadjuster of the fifth exemplary embodiment.

Data string {circumflex over ( )}5703 corresponds to the bit stringhaving length (N bits+PadNum). Six zeros each of which is surrounded bya square indicate the adjustment bit string. Data string {circumflexover ( )}503 corresponds to the N-bit code word output from the bitlength adjuster.

FIG. 87 illustrates a bit string decoder of the receiver that receivesthe modulated signal transmitted by the transmission methods of thefourth exemplary embodiment.

The detector (demodulator) generates pieces of data, such as the harddecision value, the soft decision value, the log-likelihood and thelog-likelihood ratio, which correspond to the bit of the number of bits(X+Y) of the number of first bits included in first complex signal s1and the number of second bits included in second complex signal s2, fromcomplex baseband signals x1(t) and x2(t) obtained from the receivedsignals received with the receiving antennas, and outputs data string8701 corresponding to the second bit string having the length of anintegral multiple of (X+Y). For example, data string 8701 corresponds tosecond bit string 8003 (see FIG. 83 ) having length (N− TmpPadNum).

Data string 8701 corresponding to the second bit string is input to thelog-likelihood ratio inserter in FIG. 87 , and the log-likelihood ratioinserter inserts, for example, the log-likelihood ratio (for TmpPadNum)corresponding to the adjustment bit string that is of the knowninformation deleted on the transmission side of the fourth exemplaryembodiment in data string 8701 corresponding to the second bit string,and outputs adjusted data string 8702. Accordingly, adjusted data string8702 becomes the N data strings.

Adjusted data string 8702 is input to the deinterleaver in FIG. 87 , andthe deinterleaver rearranges the data, and outputs rearranged datastring 8703.

Rearranged data string 8703 is input to the error correction decoder inFIG. 87 , and the error correction decoder performs the error correctiondecoding (for example, the BP (Belief Propagation) decoding (such assum-product decoding, min-sum decoding, Normalized BP decoding andoffset BP decoding) or the Bit Flipping decoding for the use of the LDPCcode) to obtain the K-bit information bit estimation series. Theknown-information deleter obtains and outputs data 8704 in which theknown information is deleted from the K-bit information bit estimationseries.

In the case that the bit interleaver is used on the transmission side,the deinterleaver is inserted as illustrated in FIG. 87 . On the otherhand, in the case that the bit interleaver is used on the transmissionside, the necessity of the deinterleaver in FIG. 87 is eliminated.

Effect of Fifth Exemplary Embodiment

The action of the receiver in transmitting the modulated signal by thetransmission methods of the first to fourth exemplary embodiments isdescribed with reference to FIGS. 85 and 87 .

In the receiver, the action of the receiver is changed to perform theerror correction coding based on the pieces of information correspondingto the modulation schemes of s1 (t) and s2(t) that are used in thetransmitter, so that there is a high possibility of being able to obtainthe high data reception quality.

When the encoder outputs the code word of the error correction codehaving the N-bit code word length (block length (code length)), thenumber of bits (X+Y) that can be transmitted at the identical frequencyand the identical time using first and second complex signals s1 and s2does not include the data of the plurality of blocks (of the errorcorrection code) irrespective of the value of N with respect to a set ofcomplex signals based on any combination of the modulation schemes, andtherefore the error correction decoder properly performs thedemodulation and the decoding to enhance a possibility of being able toreduce the memory of the receiver.

Sixth Exemplary Embodiment

FIG. 88 illustrates a bit string decoder of a receiver according to asixth exemplary embodiment.

The operations of the deinterleaver and detector are identical to thoseof the fifth exemplary embodiment.

The detector outputs bit string {circumflex over ( )}6003 in which oneof the adjustment bit strings of the first to ninth modifications of thesecond exemplary embodiment is inserted.

The bit length adjuster of the sixth exemplary embodiment extracts thedata string (for example, the log-likelihood ratio corresponding to thesecond bit string) corresponding to the second bit string and partialdata (for example, the log-likelihood ratio) corresponding to the bitvalue in a predetermined art of the N bits.

For example, the bit string adjuster performs the following processingin order to obtain the high error correction ability.

The data corresponding to the adjustment bit string is selectivelyextracted from bit string {circumflex over ( )}6003 having (N+TmpPadNum)bits.

For example, log-likelihood ratio Additional_Prob associated with theadjustment bit string is generated from the data corresponding to eachbit of the adjustment bit string.

Generated AdditionalProb is supplied to the error correction decoder.

The error correction decoder estimates the N-bit code word of the errorcorrection code using AdditionalProb and the partial data (for example,the log-likelihood ratio) corresponding to the bit value of thepredetermined part in the N bits.

At this point, for example, the error correction decoder performs thesum-product decoding based on the Taner graph structure (parity checkmatrix) of the second exemplary embodiment.

FIG. 89 is a view conceptually illustrating processing of the sixthexemplary embodiment.

In FIG. 89 , a circle or a square indicate the same information as thesecond exemplary embodiment.

In FIG. 89 , second bit string {circumflex over ( )}6003 having bitlength (N+padNum) is output from the demapper.

In FIG. 89 , bit string {circumflex over ( )}503 having bit length N isoutput from the bit length adjuster. In FIG. 89 , Additional_Prob is anadditional log-likelihood ratio obtained from, for example, thelog-likelihood ratio of the adjustment bit string. The log-likelihoodratio of the predetermined part described in the modifications of thesecond exemplary embodiment is provided using the additionallog-likelihood ratio.

For example, in the case that the predetermined part is p_last, thelog-likelihood ratio of p_last can be provided. By adding p_2ndlast tothe predetermined part, the log-likelihood ratio of p_2ndlast isprovided or the log-likelihood ratio is indirectly provided to p_last.

Therefore, the possibility of being able to obtain the high errorcorrection ability is enhanced.

Seventh Exemplary Embodiment

The transmission method and the transmission-side device are describedin the first to fourth exemplary embodiments, and the reception methodand the reception-side device are described in the fifth and sixthexemplary embodiments. The transmission method and transmission-sidedevice and the reception method and reception-side device aresupplemented in a seventh exemplary embodiment.

FIG. 90 is a view illustrating a relationship between a transmitter anda receiver in the seventh exemplary embodiment.

As illustrated in FIG. 90 , the transmitter transmits two modulatedsignals from different antennas. For example, a radio processor of thetransmitter performs pieces of processing such as OFDM signalprocessing, frequency conversion, and power amplification.

Transmitted information is input to signal generator 9001 of thetransmitter in FIG. 90 , and signal generator 9001 performs pieces ofprocessing such as coding, mapping, and precoding, and outputs precodedmodulated signals z1(t) and z2(t). Therefore, signal generator 9001performs the pieces of processing associated with the transmissionmethods of the first to fourth exemplary embodiments and the precodingprocessing.

Receiving antenna RX1 of the receiver in FIG. 90 receives a signal inwhich spaces of the signal transmitted from antenna TX1 of thetransmitter and the signal transmitted from transmitting antenna TX2 aremultiplexed.

Similarly, receiving antenna RX2 of the receiver receives a signal inwhich spaces of the signal transmitted from antenna TX1 of thetransmitter and the signal transmitted from transmitting antenna TX2multiplexed.

In a channel estimator of the receiver in FIG. 90 , each antennaestimates channel fluctuations of modulated signals z1(t) and z2(t).

Signal processor 9002 of the receiver in FIG. 90 performs the receptionprocessing of the fifth and sixth exemplary embodiments and the like. Asa result, the receiver obtains the estimation result of the transmittedinformation from the transmitter.

The seventh exemplary embodiment is described while applied to the firstto sixth exemplary embodiments. The description of the transmitter inFIG. 90 is made in the case that the transmission method and thetransmission-side device are described in the following exemplaryembodiments, and the description of the receiver in FIG. 90 is made inthe case that the reception method and the reception-side device aredescribed.

Eighth Exemplary Embodiment

Modifications of “the adjustment method in which the excess portion isshortened such that the bit length is the multiple of the value of(X+Y)” of the fourth exemplary embodiment will be described in an eighthexemplary embodiment.

Example 1

FIG. 91 illustrates a configuration of a transmission-side modulator ofthe eighth exemplary embodiment. In FIG. 91 , the component similar tothat of the first to seventh exemplary embodiments is designated by theidentical reference mark.

Control information 512 and K-bit information 501 of ith block are inputto encoder 502, and encoder 502 performs the error correction codingsuch as the LDPC coding to output N-bit code word 503 of the ith blockbased on the pieces of information about the scheme, coding rate, andblock length (code length) of the error correction code included incontrol information 512.

Control information 512 and N-bit code word 503 of the ith block areinput to bit length adjuster 9101, and bit length adjuster 9101 decidesthe number of bits PunNum deleted from N-bit code word 503 based on thepieces of information about the modulation schemes of s1(t) and s2(t)included in control information 512 or the value of (X+Y), deletes thePunNum-bit data from N-bit code word 503, and outputs (N− PunNum)-bitdata string 9102. Similarly to the first to seventh exemplaryembodiments, PunNum is decided such that (N− PunNum) is a multiple ofthe value of (X+Y) (sometimes PunNum becomes 0 (zero) depending on thevalue of (X+Y) (the set of the first and second modulation schemes of s1(t) and s2(t)).

However, the value of (X+Y) is similar to that of the first to seventhexemplary embodiments.

Control information 512 and (N− PunNum)-bit data string 9102 are inputto mapper 504, and mapper 504 performs the mapping from the modulationschemes of s1 (t) and s2(t) included in control information 512, andoutputs first complex signal s1(t) (505A) and second complex signals2(t) (505B).

FIG. 92 illustrates the bit length of each bit string, and a squareindicates one bit. K-bit information 501 of the ith block in FIG. 91 issimilar to that in FIG. 92 .

N-bit code word 503 of the ith block in FIG. 91 is similar to that inFIG. 92 . PunNum bits are selected and deleted from N-bit code word 503of the ith block to generate (N− PunNum)-bit data string 9102 (see FIG.92 ).

Example 2

FIG. 93 illustrates a configuration of a modulator different from thatin FIG. 91 in the eighth exemplary embodiment. In FIG. 93 , thecomponent similar to that of the first to seventh exemplary embodimentsis designated by the identical reference mark.

Control information 512 and K-bit information 501 of ith block are inputto encoder 502, and encoder 502 performs the error correction codingsuch as the LDPC coding to output N-bit code word 503 of the ith blockbased on the pieces of information about the scheme, coding rate, andblock length (code length) of the error correction code included incontrol information 512.

Control information 512 and N-bit code word 503 of the ith block areinput to bit interleaver 9103, and bit interleaver 9103 rearranges theN-bit code word of the ith block based on the information about theinterleaving method included in control information 512, and outputsinterleaved N-bit code word 9104 of the ith block.

Control information 512 and interleaved N-bit code word 9104 of the ithblock are input to bit length adjuster 9101, and bit length adjuster9101 decides the number of bits PunNum deleted from interleaved N-bitcode word 9104 based on the pieces of information about the modulationschemes of s1(t) and s2(t) included in control information 512 or thevalue of (X+Y), deletes the PunNum-bit data from interleaved N-bit codeword 9104 of the ith block, and outputs (N− PunNum)-bit data string9102. Similarly to the first to seventh exemplary embodiments, PunNum isdecided such that (N− PunNum) is a multiple of the value of (X+Y)(sometimes PunNum becomes 0 (zero) depending on the value of (X+Y) (theset of the first and second modulation schemes of s1 (t) and s2(t)).

However, the value of (X+Y) is similar to that of the first to seventhexemplary embodiments.

Control information 512 and (N− PunNum)-bit data string 9102 are inputto mapper 504, and mapper 504 performs the mapping from the modulationschemes of s1 (t) and s2(t) included in control information 512, andoutputs first complex signal s1(t) (505A) and second complex signals2(t) (505B).

FIG. 94 illustrates the bit length of each bit string, and a squareindicates one bit. K-bit information 501 of the ith block in FIG. 94 issimilar to that in FIG. 93 .

N-bit code word 503 of the ith block in FIG. 93 is similar to that inFIG. 94 . Then, as illustrated in FIG. 94 , the bit interleaving,namely, the bit rearrangement is performed on N-bit code word 503 of theith block to generate interleaved N-bit code word 9104 of the ith block.

PunNum bits are selected and deleted from interleaved N-bit code word9104 of the ith block to generate (N− PunNum)-bit data string 9102 (seeFIG. 94 ).

Effect

As described above, PunNum is decided such that (N− PunNum) is themultiple of the value of (X+Y) in (N− PunNum)-bit data string 9102output from bit length adjuster 9101.

Therefore, when the encoder outputs the code word of the errorcorrection code having the N-bit code word length (block length (codelength)), because (N− PunNum) is the multiple of the value of (X+Y)irrespective of the value of N with respect to a set of complex signalsbased on any combination of the modulation schemes, the number of bits(X+Y) that can be transmitted at the identical frequency and theidentical time using first and second complex signals s1 and s2 does notinclude the data of the plurality of blocks (of the error correctioncode). Therefore, there is a high possibility of reducing the memory ofthe transmitter and/or receiver.

In the case that the value of (X+Y), namely, the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t) isswitched (or in the case that the setting of the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t)can be changed), bit length adjuster 9101 is disposed at the stagesubsequent to bit interleaver 9103 as illustrated in FIG. 93 , whichallows the memory size of the bit interleaver to be kept constantirrespective of the set of the first modulation schemes of s1(t) and thesecond modulation scheme of s2(t). Therefore, the increase in memorysize of the bit interleaver can be prevented. (When the order of bitlength adjuster 9101 and bit interleaver 9103 becomes reversed, it isnecessary to change the memory size due to the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t).For this reason, it is necessary to dispose bit length adjuster 9101 atthe stage subsequent to bit interleaver 9103. In FIG. 93 , bit lengthadjuster 9101 is disposed just behind bit interleaver 9103.Alternatively, an interleaver that performs another piece ofinterleaving or another processor may be inserted between bitinterleaver 9103 and bit length adjuster 9101.

A plurality of code word lengths (block lengths (code lengths)) of theerror correction code may be prepared. For example, it is assumed thatNa bits and Nb bits are prepared as the code word length (block length(code length)) of the error correction code. When the error correctioncode of the Na-bit code word length (block length (code length)) isused, the memory size of the bit interleaver is set to the Na bits, thebit interleaving is performed, and bit length adjuster 9101 in FIG. 93deletes the necessary number of bits as needed. Similarly, when theerror correction code of the Nb-bit code word length (block length (codelength)) is used, the memory size of the bit interleaver is set to theNb bits, the bit interleaving is performed, and bit length adjuster 9101in FIG. 93 deletes the necessary number of bits as needed.

Example 3

FIG. 93 illustrates a configuration of a modulator different from thatin FIG. 91 in the eighth exemplary embodiment. In FIG. 93 , thecomponent similar to that of the first to seventh exemplary embodimentsis designated by the identical reference mark.

Control information 512 and K-bit information 501 of ith block are inputto encoder 502, and encoder 502 performs the error correction codingsuch as the LDPC coding to output N-bit code word 503 of the ith blockbased on the pieces of information about the scheme, coding rate, andblock length (code length) of the error correction code included incontrol information 512.

Control information 512 and z N-bit code words, namely, (N×z) bits (z isan integer of 1 or more) are input to bit interleaver 9103, and bitinterleaver 9103 rearranges the (N× z) bits based on the informationabout the interleaving method included in control information 512, andoutputs interleaved N-bit code word 9104.

Control information 512 and interleaved N-bit code word 9104 are inputto bit length adjuster 9101, and bit length adjuster 9101 decides thenumber of bits PunNum deleted from interleaved bit string 9104 based onthe pieces of information about the modulation schemes of s1(t) ands2(t) included in control information 512 or the value of (X+Y), deletesthe PunNum-bit data from interleaved bit string 9104, and outputs (N×z−PunNum)-bit data string 9102.

Similarly to the first to seventh exemplary embodiments, PunNum isdecided such that (N×z−PunNum) is a multiple of the value of (X+Y)(sometimes PunNum becomes 0 (zero) depending on the value of (X+Y) (theset of the first and second modulation schemes of s1 (t) and s2(t)).

However, the value of (X+Y) is similar to that of the first to seventhexemplary embodiments.

Control information 512 and (N×z−PunNum)-bit data string 9102 are inputto mapper 504, and mapper 504 performs the mapping from the modulationschemes of s1(t) and s2(t) included in control information 512, andoutputs first complex signal s1(t) (505A) and second complex signals2(t) (505B).

FIG. 95 illustrates the bit length of each bit string, and a squareindicates one bit. In FIG. 95 , reference mark 501 designates z bundlesof the pieces of K-bit information.

Z N-bit code words 503 in FIG. 95 is similar to that in FIG. 94 . Then,as illustrated in FIG. 95 , the bit interleaving, namely, the bitrearrangement is performed on z N-bit code words 503 to generateinterleaved (N×z)-bit bit string 9104.

PunNum bits are selected and deleted from interleaved (N×z)-bit bitstring 9104 to generate (N×z−PunNum)-bit data string 9102 (see FIG. 95).

Effect

As described above, PunNum is decided such that (N×z−PunNum) is themultiple of the value of (X+Y) in (N×z−PunNum)-bit data string 9102output from bit length adjuster 9101.

Therefore, when the encoder outputs the code word of the errorcorrection code having the N-bit code word length (block length (codelength)), because (N− PunNum) is the multiple of the value of (X+Y)irrespective of the value of N with respect to a set of complex signalsbased on any combination of the modulation schemes, the number of bits(X+Y) that can be transmitted at the identical frequency and theidentical time using first and second complex signals s1 and s2 does notinclude the data of the blocks except for the z code words. Therefore,there is a high possibility of reducing the memory of the transmitterand/or receiver.

In the case that the value of (X+Y), namely, the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t) isswitched (or in the case that the setting of the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t)can be changed), bit length adjuster 9101 is disposed at the stagesubsequent to bit interleaver 9103 as illustrated in FIG. 93 , whichallows the memory size of the bit interleaver to be kept constantirrespective of the set of the first modulation schemes of s1(t) and thesecond modulation scheme of s2(t). Therefore, the increase in memorysize of the bit interleaver can be prevented. (When the order of bitlength adjuster 9101 and bit interleaver 9103 becomes reversed, it isnecessary to change the memory size due to the set of the firstmodulation schemes of s1(t) and the second modulation scheme of s2(t).For this reason, it is necessary to dispose bit length adjuster 9101 atthe stage subsequent to bit interleaver 9103. In FIG. 93 , bit lengthadjuster 9101 is disposed just behind bit interleaver 9103.Alternatively, an interleaver that performs another piece ofinterleaving or another processor may be inserted between bitinterleaver 9103 and bit length adjuster 9101.

A plurality of code word lengths (block lengths (code lengths)) of theerror correction code may be prepared. For example, it is assumed thatNa bits and Nb bits are prepared as the code word length (block length(code length)) of the error correction code. When the error correctioncode of the Na-bit code word length (block length (code length)) isused, the memory size of the bit interleaver is set to the Na bits, thebit interleaving is performed, and bit length adjuster 9101 in FIG. 93deletes the necessary number of bits as needed. Similarly, when theerror correction code of the Nb-bit code word length (block length (codelength)) is used, the memory size of the bit interleaver is set to theNb bits, the bit interleaving is performed, and bit length adjuster 9101in FIG. 93 deletes the necessary number of bits as needed.

A plurality of bit interleaving sizes may be prepared with respect tothe code length (block length (code length)) of each error correctioncode. For example, when the error correction code has the N-bit codeword length, (N×a) bits and (N×b) bits are prepared as the bitinterleaving size (a and b are an integer of 1 or more). When the (N×a)bits are used as the bit interleaving size, the bit interleaving isperformed, and bit length adjuster 9101 in FIG. 93 deletes the necessarynumber of bits as needed. Similarly, when the (N× b) bits are used asthe bit interleaving size, the bit interleaving is performed, and bitlength adjuster 9101 in FIG. 93 deletes the necessary number of bits asneeded.

Ninth Exemplary Embodiment

An action of the receiver that receives the modulated signal transmittedby the transmission method of the eighth exemplary embodiment,particularly the bit string decoder will be described in a ninthexemplary embodiment.

That is, modulation (detection) processing is performed on complexsignals s1(t) and s2(t), which are generated from (information) bitstring 501 by “the section that generates the modulated signal”(modulator) of the eighth exemplary embodiment and transmitted after thepieces of processing such as the MIMO pre-coding, and the bit string isrestored from complex signals (x1(t) and x2(t)).

Complex signals x1(t) and x2(t) are a complex baseband signal obtainedfrom the received signal received each receiving antenna.

FIG. 96 illustrates a bit string decoder of the receiver that receivesthe modulated signal transmitted by the transmission methods of theeighth exemplary embodiment.

In FIG. 85 , “{circumflex over ( )}” (caret) indicates an estimationresult of the signal having the reference mark under the caret,hereinafter, the caret is omitted by adding “{circumflex over ( )}” tothe reference mark.

The bit string decoder in FIG. 96 includes a detector (demodulator), abit length adjuster, and an error correction decoder.

The detector (demodulator) in FIG. 96 generates pieces of data, such asthe hard decision value, the soft decision value, the log-likelihood andthe log-likelihood ratio, which correspond to the bit of the number ofbits (X+Y) of the number of first bits included in first complex signals1 and the number of second bits included in second complex signal s2,from complex baseband signals x1(t) and x2(t) obtained from the receivedsignals received with the receiving antennas, and outputs data string9601 corresponding to the (N− PunNum)-bit data string or(N×z−PunNum)-bit data string 9102, which is of the length of theintegral multiple of (X+Y).

Data string 9601 corresponding to the (N− PunNum)-bit data string or(N×z −PunNum)-bit data string 9102 is input to the log-likelihood ratioinserter in FIG. 96 , and the log-likelihood ratio inserter inserts thelog-likelihood ratio of each of the PunNum bits deleted on thetransmission side, namely, the PunNum log-likelihood ratios in datastring 9601 corresponding to the (N− PunNum)-bit data string or(N×z−PunNum)-bit data string 9102, and outputs N or (N×z) log-likelihoodratio series 9602.

N or (N×z) log-likelihood ratio series 9602 are input to thedeinterleaver in FIG. 96 , and the deinterleaver performs thedeinterleaving to output N or (N×z) deinterleaved log-likelihood ratioseries 9603.

N or (N×z) deinterleaved log-likelihood ratio series 9603 is input tothe error correction decoder in FIG. 96 , and the error correctiondecoder performs the error correction decoding (for example, BP (BeliefPropagation) decoding (such as sum-product decoding, min-sum decoding,Normalized BP decoding and offset BP decoding) or Bit Flipping decodingfor the use of the LDPC code) to obtain the K-bit or (K×z)-bitinformation bit estimation series.

In the case that the bit interleaver is used on the transmission side,the deinterleaver is inserted as illustrated in FIG. 96 . On the otherhand, in the case that the bit interleaver is used on the transmissionside, the necessity of the deinterleaver in FIG. 96 is eliminated.

Effect of Ninth Exemplary Embodiment

The action of the receiver in transmitting the modulated signal by thetransmission methods of the eighth exemplary embodiment is describedwith reference to FIG. 96 .

In the receiver, the action of the receiver is changed to perform theerror correction coding based on the pieces of information correspondingto the modulation schemes of s1 (t) and s2(t) that are used in thetransmitter, so that there is a high possibility of being able to obtainthe high data reception quality.

When the encoder outputs the code word of the error correction codehaving the N-bit code word length (block length (code length)), thenumber of bits (X+Y) that can be transmitted at the identical frequencyand the identical time using first and second complex signals s1 and s2does not include the data of the plurality of blocks (of the errorcorrection code) irrespective of the value of N with respect to a set ofcomplex signals based on any combination of the modulation schemes, andtherefore the error correction decoder properly performs thedemodulation and the decoding to enhance a possibility of being able toreduce the memory of the receiver.

Tenth Exemplary Embodiment

The bit length adjusting method widely applied to the precoding methodis described above. A bit length adjusting method using a transmissionmethod in which the phase change is regularly performed after theprecoding will be described in a tenth exemplary embodiment.

FIG. 97 is a view illustrating a section that performsprecoding-associated processing in the transmitter of the tenthexemplary embodiment.

Referring to FIG. 97 , bit series 9701 and control signal 9712 are inputto mapper 9702. It is assumed that control signal 9712 assigns thetransmission of the two streams as a transmission scheme. Additionally,it is assumed that control signal 9712 assigns modulation scheme α andmodulation scheme β as respective modulation schemes of the two streams.It is assumed that modulation scheme α is a modulation scheme formodulating x-bit data, and that modulation scheme β is a modulationscheme for modulating y-bit data (for example, a modulation scheme formodulating 4-bit data for 16QAM (16 Quadrature Amplitude Modulation),and a modulation scheme for modulating 6-bit data for 64QAM (64Quadrature Amplitude Modulation)).

Mapper 9702 modulates the x-bit data in (x+y)-bit data using modulationscheme α to generate and output baseband signal s₁(t) (9703A), andmodulates the y-bit data using modulation scheme β to output basebandsignal s₂(t) (9703B). (One mapper is provided in FIG. 97 .Alternatively, a mapper that generates baseband signal s₁(t) and amapper that generates baseband signal s₂(t) may separately be provided.At this point, bit series 9701 is divided in the mapper that generatesbaseband signal s₁(t) and the mapper that generates baseband signals₂(t).)

Each of s₁(t) and s₂(t) is represented as a complex number (however, maybe one of a complex number and a real number), and t is time. For thetransmission scheme in which multi-carrier such as OFDM (OrthogonalFrequency Division Multiplexing) is used, it can also be considered thats₁ and s₂ are a function of frequency f like s₁(f) and s₂(f) or that s₁and s₂ are a function of time t and frequency f like s₁(t,f) ands₂(t,f).

Hereinafter, the baseband signal, a precoding matrix, a phase change,and the like are described as the function of time t. Alternatively, thebaseband signal, the precoding matrix, the phase change, and the likemay be considered to be the function of frequency f or the function oftime t and frequency f.

Accordingly, sometimes the baseband signal, the precoding matrix, thephase change, and the like are described as a function of symbol numberi. In this case, the baseband signal, the precoding matrix, the phasechange, and the like may be considered to be the function of time t, thefunction of frequency f, or the function of time t and frequency f. Thatis, the symbol and the baseband signal may be generated and disposed ineither a time-axis direction or a frequency-axis direction. The symboland the baseband signal may be generated and disposed in the time-axisdirection and the frequency-axis direction.

Baseband signal s₁(t) (9703A) and control signal 9712 are input to powerchanger 9704A (power adjuster 9704A), and power changer 9704A (poweradjuster 9704A) sets real number P₁ based on control signal 9712, andoutputs (P₁×s₁(t)) as power-changed signal 9705A (P₁ may be a complexnumber).

Similarly, baseband signal s₂(t) (9703B) and control signal 9712 areinput to power changer 9704B (power adjuster 9704B), and power changer9704B (power adjuster 9704B) sets real number P₂, and outputs (P₂×s₂(t))as power-changed signal 9705B (P₂ may be a complex number).

Power-changed signal 9705A, power-changed signal 9705B, and controlsignal 9712 are input to weighting synthesizer 9706, and weightingsynthesizer 9706 sets precoding matrix F (or F(i)) based on controlsignal 9712. Assuming that i is a slot number (symbol number), weightingsynthesizer 9706 performs the following calculation.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 357} \right\rbrack} & \; \\{\begin{pmatrix}{u_{1}(i)} \\{u_{2}(i)}\end{pmatrix} = {{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {{\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & \left( {{R10}\text{-}1} \right)\end{matrix}$

In the formula, each of a, b, c, and d is represented as a complexnumber (may be represented as a real number), and at least three of a,b, c, and d must not be 0 (zero), where each of a, b, c, and d is acoefficient that depends on the decision of the set of modulationschemes of s₁(t) and s₂(t).

Weighting synthesizer 9706 outputs u₁(i) in equation (R10-1) asweighting-synthesized signal 9707A, and outputs u₂(i) in equation(R10-1) as weighting-synthesized signal 9707B.

u₂(i) (weighting-synthesized signal 9707B) in equation (R10-1) andcontrol signal 9712 are input to phase changer 9708, and phase changer9708 changes the phase of u₂(i) (weighting-synthesized signal 9707B) inequation (R10-1) based on control signal 9712.

Accordingly, the signal in which the phase of u₂(i)(weighting-synthesized signal 9707B) in equation (R10-1) is changed isrepresented as (e^(jθ(i))×u₂(i)), and phase changer 9708 outputs(e^(jθ(i))×u₂(i)) as phase-changed signal 9709 (j is an imaginary unit).The changed phase constitutes a characteristic portion that the changedphase is the function of i like θ(i).

Weighting-synthesized signal 9707A (u₁(i)) and control signal 9712 areinput to power changer 9710A, and power changer 9710A sets real numberQ₁ based on control signal 9712, and outputs (Q₁(Q₁ is a realnumber)×u₁(t)) as power-changed signal 9711A (z₁(i)) (alternatively, Q₁is a complex number).

Similarly, phase-changed signal 9709 (e^(jθ(i))×u₂(i)) and controlsignal 9712 are input to power changer 9710B, and power changer 9710Bsets real number Q₂ based on control signal 9712, and outputs (Q₂ (Q₂ isa real number)×e^(jθ(i))×u₂(t)) as power-changed signal 9711B (z₂(i))(alternatively, Q₂ is a complex number).

Accordingly, outputs z₁(i) and z₂(i) of power changers 9710A and 9710Bin FIG. 97 are given by the following equation.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 358} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} = {{\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & \left( {{R10}\text{-}2} \right)\end{matrix}$

FIG. 98 illustrates a configuration different from that in FIG. 97 as amethod for performing equation (R10-2). A difference between theconfigurations in FIGS. 97 and 98 is that the positions of the powerchanger and phase changer are exchanged (the function of changing thepower and the function of changing the phase are not changed). At thispoint, z₁(i) and z₂(i) are given by the following equation.

$\begin{matrix}{\mspace{79mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 359} \right\rbrack} & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {{\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}{F\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}}} = {{\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}{P_{1} \times {s_{1}(i)}} \\{P_{2} \times {s_{2}(i)}}\end{pmatrix}} = {\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}}} & \left( {{R10}\text{-}3} \right)\end{matrix}$

z₁(i) in equation (R10-2) is equal to z₁(i) in equation (R10-3), andz₂(i) in equation (R10-2) is equal to z₂(i) in equation (R10-3).

As to phase value θ(i) to be changed in equations (R10-2) and (R10-3),assuming that θ(i+1) −θ(i) is set to a fixed value, there is a highpossibility that the receiver obtains the good data reception quality ina radio wave propagation environment where a direct wave is dominant.However, a method for providing phase value θ(i) to be changed is notlimited to the above example. A relationship between a way to give θ(i)and the operation of the bit length adjuster is described in detaillater.

FIG. 99 illustrates a configuration example of a signal processor thatprocesses signals z₁(i) and z₂(i) obtained in FIGS. 97 to 98 .

Signal z₁(i) (9721A), pilot symbol 9722A, control information symbol9723A, and control signal 9712 are input to inserter 9724A, and inserter9724A inserts pilot symbol 9722A and control information symbol 9723A insignal (symbol) z₁(i) (9721A) according to the frame configurationincluded in control signal 9712, and outputs modulated signal 209725Aaccording to the frame configuration.

Pilot symbol 9722A and control information symbol 9723A are a symbolmodulated using BPSK (Binary Phase Shift Keying), QPSK (Quadrature PhaseShift Keying), and the like (other modulation schemes may be used).

Modulated signal 9725A and control signal 9712 are input to radiosection 9726A, and radio section 9726A performs the pieces of processingsuch as the frequency conversion and the amplification on modulatedsignal 9725A based on control signal 9712 (performs inverse Fouriertransform when the OFDM scheme is used), and outputs transmitted signal9727A as the radio wave from antenna 9728A.

Signal z₂(i) (9721B), pilot symbol 9722B, control information symbol9723B, and control signal 9712 are input to inserter 9724B, and inserter9724B inserts pilot symbol 9722B and control information symbol 9723B insignal (symbol) z₂(i) (9721B) according to the frame configurationincluded in control signal 9712, and outputs modulated signal 9725Baccording to the frame configuration.

Pilot symbol 9722B and control information symbol 9723B are a symbolmodulated using BPSK (Binary Phase Shift Keying), QPSK (Quadrature PhaseShift Keying), and the like (other modulation schemes may be used).

Modulated signal 9725B and control signal 9712 are input to radiosection 9726B, and radio section 9726B performs the pieces of processingsuch as the frequency conversion and the amplification on modulatedsignal 9725B based on control signal 9712 (performs the inverse Fouriertransform when the OFDM scheme is used), and outputs transmitted signal9727B as the radio wave from antenna 9728B.

Signals z₁(i) (9721A) and z₂(i) (9721B) having the identical number of iare transmitted from different antennas at the identical time and theidentical (common) frequency (that is, the transmission method in whichthe MIMO scheme is used).

Pilot symbols 9722A and 9722B are a symbol that is used when thereceiver performs the signal detection, the estimation of the frequencyoffset, gain control, the channel estimation, and the like. Although thesymbol is named the pilot symbol in this case, the symbol may be namedother names such as a reference symbol.

Control information symbols 9723A and 9723B are a symbol that transmitsthe information about the modulation scheme used in the transmitter, theinformation about the transmission scheme, the information about theprecoding scheme, the information about an error correction code scheme,the information about the coding rate of an error correction code, andthe information about a block length (code length) of the errorcorrection code to the receiver. The control information symbol may betransmitted using only one of control information symbols 9723A and9723B.

FIG. 100 illustrates an example of the frame configuration attime-frequency when the two streams are transmitted. In FIG. 100 , ahorizontal axis indicates a frequency, a vertical axis indicates time.FIG. 9 illustrates a configuration of the symbol from carriers 1 to 38from clock time $1 to clock time $11.

FIG. 100 simultaneously illustrates the frame configuration of thetransmitted signal transmitted from antenna 9728A in FIG. 99 and theframe of the transmitted signal transmitted from antenna 9728B in FIG.99 .

In FIG. 100 , a data symbol corresponds to signal (symbol) z₁(i) for theframe of the transmitted signal transmitted from antenna 9728A in FIG.99 . The pilot symbol corresponds to pilot symbol 9722A.

In FIG. 100 , the data symbol corresponds to signal (symbol) z₂(i) forthe frame of the transmitted signal transmitted from antenna 9728B inFIG. 99 . The pilot symbol corresponds to pilot symbol 9722B.

Accordingly, as described above, signals z₁(i) (9721A) and z₂(i) (9721B)having the identical number of i are transmitted from different antennasat the identical time and the identical (common) frequency. Theconfiguration of the pilot symbol is not limited to that in FIG. 100 .For example, a time interval and a frequency interval of the pilotsymbol are not limited to those in FIG. 100 . In FIG. 100 , the pilotsymbols are transmitted at the identical clock time and the identicalfrequency (identical (sub-) carrier) from antennas 9728A and 9728B inFIG. 99 . Alternatively, for example, the pilot symbol may be disposedin not antenna 9728B in FIG. 99 but antenna 9728A in FIG. 99 at time Aand frequency a ((sub-) carrier a), and the pilot symbol may be disposedin not antenna 9728A in FIG. 99 but antenna 9728B in FIG. 99 at time Band frequency b ((sub-) carrier b).

Although only the data symbol and the pilot symbol are illustrated inFIG. 99 , other symbols such as a control information symbol may beincluded in the frame.

Although the case that a part (or whole) of the power changer exists isdescribed with reference to FIGS. 97 and 98 , it is also considered thata part of the power changer is missing.

In the case that power changer 9704A (power adjuster 9704A) and powerchanger 9704B (power adjuster 9704B) do not exist in FIG. 97 or 98 ,z₁(i) and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 360} \right\rbrack & \; \\\begin{matrix}{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} \\{= {\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}Q_{1} & 0 \\0 & Q_{2}\end{pmatrix}\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}}\end{matrix} & \left( {{R10}\text{-}4} \right)\end{matrix}$

In the case that power changer 9710A (power adjuster 9710A) and powerchanger 9710B (power adjuster 9710B) do not exist in FIG. 97 or 98 ,z₁(i) and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 361} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}P_{1} & 0 \\0 & P_{2}\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & \left( {{R10}\text{-}5} \right)\end{matrix}$

In the case that power changer 9704A (power adjuster 9704A), powerchanger 9704B (power adjuster 9704B), power changer 9710A (poweradjuster 9710A), and power changer 9710B (power adjuster 9710B) do notexist in FIG. 97 or 98 , z₁(i) and z₂(i) are given as follows.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 362} \right\rbrack & \; \\{\begin{pmatrix}{z_{1}(i)} \\{z_{2}(i)}\end{pmatrix} = {\begin{pmatrix}1 & 0 \\0 & e^{j\;{\theta{(i)}}}\end{pmatrix}\begin{pmatrix}a & b \\c & d\end{pmatrix}\begin{pmatrix}{s_{1}(i)} \\{s_{2}(i)}\end{pmatrix}}} & \left( {{R10}\text{-}6} \right)\end{matrix}$

The relationship between the way to give θ(i) and the operation of thebit length adjuster in the precoding-associated processing will bedescribed below.

In the tenth exemplary embodiment, for example, “radian” is used in aphase unit such as an argument on a complex plane.

The use of the complex plane can display a polar coordinate of thecomplex number in terms of a polar form. Assuming that point (a, b) onthe complex plane is represented as [r,θ] in terms of the polarcoordinate when complex number z=a+jb (a and b are a real number and jis an imaginary unit) corresponds to point (a, b), the followingequation holds:a=r×cos θb=r×sin θ[Mathematical Formula 363]r=√{square root over (a ² +b ²)}  (R10-7)

where r is an absolute value of z (r=|z|) and θ is an argument, andz=a+jb is represented as r×e^(jθ).

Baseband signals s1, s2, z1, and z2 are a complex signal, and thecomplex signal is represented as I+jQ (j is an imaginary unit) when I isthe in-phase signal while Q is the quadrature signal. At this point, Imay be zero, and Q may be zero.

First, an example of the way to give θ(i) in the precoding-associatedprocessing will be described.

In the tenth exemplary embodiment, it is assumed that θ(i) is regularlychanged by way of example. Specifically, it is assumed that θ(i) isperiodically changed. It is assumed that z is a change period of θ(i) (zis an integer of 2 or more). When change period z of θ(i) is set to 9,θ(i) is changed as follows.

Change period (z=9) of θ(i) can be formed as follows.

For slot number (symbol number) i=9×k+0, θ(i=9×k+0)=0 radian

For slot number (symbol number) i=9×k+1, θ(i=9×k+1)=(2×1×π)/9 radian

For slot number (symbol number) i=9×k+2, θ(i=9×k+2)=(2×2×π)/9 radian

For slot number (symbol number) i=9×k+3, θ(i=9×k+3)=(2×3×π)/9 radian

For slot number (symbol number) i=9×k+4, θ(i=9×k+4)=(2×4×π)/9 radian

For slot number (symbol number) i=9×k+5, θ(i=9×k+5)=(2×5×π)/9 radian

For slot number (symbol number) i=9×k+6, θ(i=9×k+6)=(2×6×π)/9 radian

For slot number (symbol number) i=9×k+7, θ(i=9×k+7)=(2×7×π)/9 radian

For slot number (symbol number) i=9×k+8, θ(i=9×k+8)=(2×8×π)/9 radian

(k is an integer)

The method for forming change period (z=9) of θ(i) is not limited to theabove method. Alternatively, nine phases λ₀, λ₁, λ₂, λ₃, λ₄, λ₅, λ₆, λ₇,and λ₈ are prepared, and change period (z=9) of θ(i) may be formed asfollows.

For slot number (symbol number) i=9×k+0, θ(i=9×k+0)=λ₀ radian

For slot number (symbol number) i=9×k+1, θ(i=9×k+1)=λ₁ radian

For slot number (symbol number) i=9×k+2, θ(i=9×k+2)=λ₂ radian

For slot number (symbol number) i=9×k+3, θ(i=9×k+3)=λ₃ radian

For slot number (symbol number) i=9×k+4, θ(i=9×k+4)=λ₄ radian

For slot number (symbol number) i=9×k+5, θ(i=9×k+5)=λ₅ radian

For slot number (symbol number) i=9×k+6, θ(i=9×k+6)=λ₆ radian

For slot number (symbol number) i=9×k+7, θ(i=9×k+7)=λ₇ radian

For slot number (symbol number) i=9×k+8, θ(i=9×k+8)=λ₈ radian

(k is an integer, and 0≤λ_(v)<2π (V is an integer from 0 to 8))

There are two methods as the method for accomplishing period z=9.

(1) Assuming that x is an integer from 0 to 8 and that y is an integerfrom 0 to 8 and satisfies y≠x, λ_(x)≠λ_(y) holds in all values x and allvalues y satisfying the assumptions.

(2) Assuming that x is an integer from 0 to 8 and that y is an integerfrom 0 to 8 and satisfies y≠x, x and y satisfying λ_(x)=λ_(y) exist, andx and y form the period of 9.

Generally, in a method for forming change period z (z is an integer of 2or more) of θ(i), z phases and λ_(v) (v is an integer from 0 to (z−1))are prepared, and change period z (z is an integer of 2 or more) of θ(i)can be formed such that slot number (symbol number) i is obtained asfollows.

for i=z×k+v, θ(i=z×k+v)=λ_(v) radian

(k is an integer, and 0≤λ_(v)<2π holds.)

There are two methods as the method for accomplishing period z.

(1) Assuming that x is an integer from 0 to (z−1) and that y is aninteger from 0 to (z−1) and satisfies y≠x, λ_(x)≠λ_(y) holds in allvalues x and all values y satisfying the assumptions.

(2) Assuming that x is an integer from 0 to (z−1) and that y is aninteger from 0 to (z−1) and satisfies y≠x, x and y satisfyingλ_(x)=λ_(y) exist, and x and y form period z.

The pieces of processing before mapper 9702 in FIGS. 97 and 98 aresimilar to those of the first to ninth exemplary embodiments. Anecessary point of the tenth exemplary embodiment will be described indetail below.

Modification of First Exemplary Embodiment

In the first exemplary embodiment, the configuration of the modulatorthat performs the pieces of processing before mapper 9702 in FIGS. 97and 98 is similar to that in FIG. 57 . One of the characteristics of thefirst exemplary embodiment is that

“In order that the number of bits (X+Y) that can be transmitted by firstand second complex signals s1 and s2 transmitted at the identicalfrequency and the identical time does not include the data of theplurality of blocks (of the error correction code) with respect to theset of the complex signals based on any combination of the modulationschemes used in mapper 504 irrespective of the value of N when encoder502 in FIG. 57 outputs the code word having code word length (blocklength (code length)) N of the error correction code, first bit string503 is input to bit length adjuster 5701, the adjustment bit string isadded to the front end, the rear end, the predetermined position, andthe like of the code word of the error correction code having the codeword length (block length (code length)) N, and the second bit stringfor the mapper is output such that the number of constituting bits isthe multiple of the number of bits (X+Y)”.

The value of (X+Y) is similar to that of the first to third exemplaryembodiments.

In a modulation of the first exemplary embodiment in the tenth exemplaryembodiment, the number of bits of the adjustment bit string is decidedin consideration of change period z of θ(i). The description willspecifically be made below.

A more specific example will be described for convenience.

The error correction code used is set to the code length (block length)of 64800 bits, and change period z of θ(i) is set to 9. QPSK, 16QAM,64QAM, and 256QAM can be used as the modulation scheme. Accordingly,sets of (QPSK,QPSK), (QPSK,16QAM), (QPSK,64QAM), (QPSK,256QAM),(16QAM,16QAM), (16QAM,64QAM), (16QAM,256QAM), (64QAM,256QAM), and(256QAM,256QAM) can be considered as (modulation scheme of s₁(t) (firstcomplex signal s1), modulation scheme of s₂(t) (second complex signals2)), and some examples will be picked up and described below.

In the tenth exemplary embodiment, similarly to other exemplaryembodiments, it is assumed that both the modulation scheme of firstcomplex signal s₁ (s₁(t)) and the modulation scheme of the secondcomplex signal s2 (s₂(t)) can be switched from the plurality ofmodulation schemes.

The following definitions are given for convenience.

α is an integer of 0 or more, and β is an integer of 0 or more. A leastcommon multiple of α and β is expressed by LCM(α,β). For example,assuming that α is set to 8 and that β is set to 6, LCM(α,β) is 24.

One of the characteristics of the modulation of the first exemplaryembodiment in the tenth exemplary embodiment is that, assuming thatγ=LCM(X+Y,z) is given for the sum of the value of (X+Y), change period zof θ(i), the number of bits (N) of the code length, and the number ofbits of the adjustment bit string, a sum of the number of bits (N) ofthe code length and the number of bits of the adjustment bit string is amultiple of γ. That is, the sum of the number of bits (N) of the codelength and the number of bits of the adjustment bit string is themultiple of the least common multiple of (X+Y) and z, where X is aninteger of 1 or more, Y is an integer of 1 or more, and z is an integerof 2 or more. Accordingly, (X+Y) is an integer of 2 or more. Although itis ideal that the number of bits of the adjustment bit string is 0, andsometimes the number of bits of the adjustment bit string cannot be setto 0. At this point, it is necessary to add the adjustment bit string.

This point will be described below with an example.

Example 1

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(16QAM,16QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(8,9)=72 is obtained. Accordingly, the number ofbits of the adjustment bit string necessary to satisfy the abovecharacteristic is (72×n) bits (n is an integer of 0 or more).

FIG. 101A illustrates a state of first bit string 503 that is outputfrom encoder 502 of the modulator in FIG. 57 . In FIG. 101A, referencemark 10101 designates the ith-block code word in which the number ofbits is 64800, reference mark 10102 designates the (i+1) th-block codeword in which the number of bits is 64800, reference mark 10103designates the (i+2)th-block code word in which the number of bits is64800, reference mark 10104 designates the (i+3)th-block code word inwhich the number of bits is 64800, and the (i+4)th-block code word, the(i+5)th-block code word, and . . . are arranged.

As described above, the number of bits of the adjustment bit stringnecessary to satisfy the above characteristic is (72×n) bits (n is aninteger of 0 or more). In this case, the number of bits of theadjustment bit string is set to 0 (zero). FIG. 101B illustrates a stateof second bit string 5703 that is output from bit length adjuster 5701of the modulator in FIG. 57 . In FIG. 101B, similarly to the state offirst bit string 503 output from encoder 502 of the modulator in FIG. 57, in second bit string 5703 output from bit length adjuster 5701 of themodulator in FIG. 57 , reference mark 10101 designates the ith-blockcode word in which the number of bits is 64800, reference mark 10102designates the (i+1)th-block code word in which the number of bits is64800, reference mark 10103 designates the (i+2) th-block code word inwhich the number of bits is 64800, reference mark 10104 designates the(i+3)th-block code word in which the number of bits is 64800, and(i+4)th-block code word, (i+5)th-block code word, and . . . arearranged.

Example 2

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(64QAM,256QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(14,9)=126 is obtained. Accordingly, the numberof bits of the adjustment bit string necessary to satisfy the abovecharacteristic is (126×n+90) bits (n is an integer of 0 or more).

FIG. 102A illustrates the state of first bit string 503 that is outputfrom encoder 502 of the modulator in FIG. 57 . In FIG. 102A, referencemark 10101 designates the ith-block code word in which the number ofbits is 64800, reference mark 10102 designates the (i+1)th-block codeword in which the number of bits is 64800, reference mark 10103designates the (i+2)th-block code word in which the number of bits is64800, reference mark 10104 designates the (i+3)th-block code word inwhich the number of bits is 64800, and the (i+4)th-block code word, the(i+5)th-block code word, and . . . are arranged.

As described above, the number of bits of the adjustment bit stringnecessary to satisfy the above characteristic is (126×n+90) bits (n isan integer of 0 or more). In this case, the number of bits of theadjustment bit string is set to 90. FIG. 102B illustrates the state ofsecond bit string 5703 that is output from bit length adjuster 5701 ofthe modulator in FIG. 57 .

In FIG. 102B, reference marks 10201, 10202, and 10203 designate theadjustment bit string. Adjustment bit string 10201 is used in ith-blockcode word 10101 in which the number of bits is 64800, and the number ofbits of adjustment bit string 10201 is 90 bits. Accordingly, a total ofthe numbers of bits of ith-block code word 10101 and adjustment bitstring 10201 is 64890 bits. Therefore, the effect of the first exemplaryembodiment can be obtained. The sum of code word 10101 of the ith blockhaving 64800 bits and the number of bits of adjustment bit string 10201is the number of slots necessary for the transmission of 64890 bits (inthis case, one slot means one formed by one symbol of s1 and one symbolof s2), and is an integral multiple of change period (z=9) of θ(i).

Therefore, in the slot having 64890 bits that is of the sum of code word10101 in the ith block having 64800 bits and the number of bits ofadjustment bit string 10201, the number of occurrences of nine valuesthat can be taken by θ(i) are equal to one another, so that apossibility of obtaining the information included in code word 10101 ofthe ith block with high reception quality can be enhanced.

Similarly, adjustment bit string 10202 is used in code word 10102 in(i+1)-th-block having 64800 bits, and adjustment bit string 10202 has 90bits. Accordingly, the total of the numbers of bits of (i+1)th-blockcode word 10102 and adjustment bit string 10202 is 64890 bits.Therefore, the effect of the first exemplary embodiment can be obtained.The sum of code word 10102 of the (i+1)th block having 64800 bits andthe number of bits of adjustment bit string 10202 is an integralmultiple of period (z=9) of the change in the number of slots θ(i)necessary for the transmission of 64890 bits. Therefore, in the slothaving 64890 bits that is of the sum of code word 10102 in the (i+1)thblock having 64800 bits and the number of bits of adjustment bit string10202, the number of occurrences of nine values that can be taken byθ(i) are equal to one another, so that a possibility of obtaining theinformation included in code word 10102 of the (i+1)th block with highreception quality can be enhanced.

Similarly, adjustment bit string 10203 is used in code word 10103 in the(i+2)th-block having 64800 bits, and adjustment bit string 10203 has 90bits. Accordingly, the total of the numbers of bits of (i+2)th-blockcode word 10103 and adjustment bit string 10203 is 64890 bits.Therefore, the effect of the first exemplary embodiment can be obtained.The sum of code word 10103 of the (i+2)th block having 64800 bits andthe number of bits of adjustment bit string 10203 is an integralmultiple of period (z=9) of the change in the number of slots θ(i)necessary for the transmission of 64890 bits. Therefore, in the slothaving 64890 bits that is of the sum of code word 10103 in the (i+2)thblock having 64800 bits and the number of bits of adjustment bit string10203, the number of occurrences of nine values that can be taken byθ(i) are equal to one another, so that a possibility of obtaining theinformation included in code word 10103 of the (i+2)th block with highreception quality can be enhanced.

The adjustment bit string inserting method is not limited to that inFIG. 102 , but the total of 64890 bits of the code word having the 64800bits and the adjustment bit string having the 90 bits may be arranged inany order.

Modification of Second Exemplary Embodiment

In the second exemplary embodiment, the configuration of the modulatorthat performs the pieces of processing before mapper 9702 in FIGS. 97and 98 is similar to that in FIG. 60 . One of the characteristics of thesecond exemplary embodiment is that “In order that the number of bits(X+Y) that can be transmitted by first and second complex signals s1 ands2 transmitted at the identical frequency and the identical time doesnot include the data of the plurality of blocks (of the error correctioncode) with respect to the set of the complex signals based on anycombination of the modulation schemes used in mapper 504 irrespective ofthe value of N when encoder 502LA in FIG. 60 outputs the code wordhaving code word length (block length (code length)) N of the errorcorrection code, first bit string 503 is input to bit length adjuster6001, the adjustment bit string is added to the front end, the rear end,the predetermined position, and the like of the code word of the errorcorrection code having the code word length (block length (code length))N, and the second bit string for the mapper is output such that thenumber of constituting bits is the multiple of the number of bits (X+Y).The adjustment bit string is constructed by repeating the bit value in apredetermined portion of the N-bit code word obtained through the codingprocessing at least once (repetition)”.

The value of (X+Y) is similar to that of the first to third exemplaryembodiments.

In a modulation of the second exemplary embodiment in the tenthexemplary embodiment, the number of bits of the adjustment bit string isdecided in consideration of change period z of θ(i). The descriptionwill specifically be made below.

A more specific example will be described for convenience.

The error correction code used is set to the code length (block length)of 64800 bits, and change period z of θ(i) is set to 9. QPSK, 16QAM,64QAM, and 256QAM can be used as the modulation scheme. Accordingly,sets of (QPSK,QPSK), (QPSK,16QAM), (QPSK,64QAM), (QPSK,256QAM),(16QAM,16QAM), (16QAM,64QAM), (16QAM,256QAM), (64QAM,256QAM), and(256QAM,256QAM) can be considered as (modulation scheme of s₁(t) (firstcomplex signal s1), modulation scheme of s₂(t) (second complex signals2)), and some examples will be picked up and described below.

In the tenth exemplary embodiment, similarly to other exemplaryembodiments, it is assumed that both the modulation scheme of firstcomplex signal s1 (s₁(t)) and the modulation scheme of the secondcomplex signal s2 (s₂(t)) can be switched from the plurality ofmodulation schemes.

One of the characteristics of the modulation of the second exemplaryembodiment in the tenth exemplary embodiment is that, assuming thatγ=LCM(X+Y,z) is given for the sum of the value of (X+Y), change period zof θ(i), the number of bits (N) of the code length, and the number ofbits of the adjustment bit string, a sum of the number of bits (N) ofthe code length and the number of bits of the adjustment bit string is amultiple of γ. That is, the sum of the number of bits (N) of the codelength and the number of bits of the adjustment bit string is themultiple of the least common multiple of (X+Y) and z, where X is aninteger of 1 or more, Y is an integer of 1 or more, and z is an integerof 2 or more. Accordingly, (X+Y) is an integer of 2 or more. Although itis ideal that the number of bits of the adjustment bit string is 0, andsometimes the number of bits of the adjustment bit string cannot be setto 0. At this point, it is necessary to add the adjustment bit string.

This point will be described below with an example.

Example 3

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(16QAM,16QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(8,9)=72 is obtained. Accordingly, the number ofbits of the adjustment bit string necessary to satisfy the abovecharacteristic is (72×n) bits (n is an integer of 0 or more).

FIG. 101A illustrates the state of first bit string 503 that is outputfrom encoder 502LA of the modulator in FIG. 60 . In FIG. 101A, referencemark 10101 designates the ith-block code word in which the number ofbits is 64800, reference mark 10102 designates the (i+1)th-block codeword in which the number of bits is 64800, reference mark 10103designates the (i+2)th-block code word in which the number of bits is64800, reference mark 10104 designates the (i+3)th-block code word inwhich the number of bits is 64800, and the (i+4)th-block code word, the(i+5)th-block code word, and . . . are arranged.

As described above, the number of bits of the adjustment bit stringnecessary to satisfy the above characteristic is (72×n) bits (n is aninteger of 0 or more).

In this case, the number of bits of the adjustment bit string is set to0 (zero). FIG. 101B illustrates the state of second bit string 6003 thatis output from bit length adjuster 6001 of the modulator in FIG. 60 . InFIG. 101B, similarly to the state of first bit string 503 output fromEncoder 502LA in FIG. 60 , in second bit string 6003 output from bitlength adjuster 6001 of the modulator in FIG. 60 , reference mark 10101designates the ith-block code word in which the number of bits is 64800,reference mark 10102 designates the (i+1)th-block code word in which thenumber of bits is 64800, reference mark 10103 designates the(i+2)th-block code word in which the number of bits is 64800, referencemark 10104 designates the (i+3)th-block code word in which the number ofbits is 64800, and (i+4)th-block code word, (i+5)th-block code word, and. . . are arranged.

Example 4

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(64QAM,256QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(14,9)=126 is obtained. Accordingly, the numberof bits of the adjustment bit string necessary to satisfy the abovecharacteristic is (126×n+90) bits (n is an integer of 0 or more).

FIG. 102A illustrates the state of first bit string 503 that is outputfrom encoder 502LA of the modulator in FIG. 60 . In FIG. 102A, referencemark 10101 designates the ith-block code word in which the number ofbits is 64800, reference mark 10102 designates the (i+1)th-block codeword in which the number of bits is 64800, reference mark 10103designates the (i+2)th-block code word in which the number of bits is64800, reference mark 10104 designates the (i+3)th-block code word inwhich the number of bits is 64800, and the (i+4)th-block code word, the(i+5)th-block code word, and . . . are arranged.

As described above, the number of bits of the adjustment bit stringnecessary to satisfy the above characteristic is (126×n+90) bits (n isan integer of 0 or more). In this case, the number of bits of theadjustment bit string is set to 90. FIG. 102B illustrates the state ofsecond bit string 6003 that is output from bit length adjuster 6001 ofthe modulator in FIG. 60 .

In FIG. 102B, reference marks 10201, 10202, and 10203 designate theadjustment bit string. Adjustment bit string 10201 is used in code word10101 in the ith-block code having 64800 bits, and adjustment bit string10201 has 90 bits. Accordingly, a total of the numbers of bits ofith-block code word 10101 and adjustment bit string 10201 is 64890 bits.Therefore, the effect of the second exemplary embodiment can beobtained. The sum of code word 10101 of the ith block having 64800 bitsand the number of bits of adjustment bit string 10201 is the number ofslots necessary for the transmission of 64890 bits (in this case, oneslot means one formed by one symbol of s1 and one symbol of s2), and isan integral multiple of change period (z=9) of θ(i).

Therefore, in the slot having 64890 bits that is of the sum of code word10101 in the ith block having 64800 bits and the number of bits ofadjustment bit string 10201, the number of occurrences of nine valuesthat can be taken by θ(i) are equal to one another, so that apossibility of obtaining the information included in code word 10101 ofthe ith block with high reception quality can be enhanced.

Similarly, adjustment bit string 10202 is used in code word 10102 in the(i+1) th-block having 64800 bits, and adjustment bit string 10202 has 90bits. Accordingly, the total of the numbers of bits of (i+1)th-blockcode word 10102 and adjustment bit string 10202 is 64890 bits.Therefore, the effect of the second exemplary embodiment can beobtained. The sum of code word 10102 of the (i+1)th block having 64800bits and the number of bits of adjustment bit string 10202 is anintegral multiple of period (z=9) of the change in the number of slotsθ(i) necessary for the transmission of 64890 bits. Therefore, in theslot having 64890 bits that is of the sum of code word 10102 in the(i+1)th block having 64800 bits and the number of bits of adjustment bitstring 10202, the number of occurrences of nine values that can be takenby θ(i) are equal to one another, so that a possibility of obtaining theinformation included in code word 10102 of the (i+1)th block with highreception quality can be enhanced.

Similarly, adjustment bit string 10203 is used in code word 10103 in the(i+2) th-block having 64800 bits, and adjustment bit string 10203 has 90bits. Accordingly, the total of the numbers of bits of (i+2)th-blockcode word 10103 and adjustment bit string 10203 is 64890 bits.Therefore, the effect of the second exemplary embodiment can beobtained. The sum of code word 10103 of the (i+2)th block having 64800bits and the number of bits of adjustment bit string 10203 is anintegral multiple of period (z=9) of the change in the number of slotsθ(i) necessary for the transmission of 64890 bits. Therefore, in theslot having 64890 bits that is of the sum of code word 10103 in the(i+2)th block having 64800 bits and the number of bits of adjustment bitstring 10203, the number of occurrences of nine values that can be takenby θ(i) are equal to one another, so that a possibility of obtaining theinformation included in code word 10103 of the (i+2)th block with highreception quality can be enhanced.

As described in the second exemplary embodiment, the adjustment bitstring is constructed by repeating the bit value in a predeterminedportion of the N-bit code word obtained through the coding processing atleast once (repetition). The specific method for constructing theadjustment bit string is described in the second exemplary embodiment.

The adjustment bit string inserting method is not limited to that inFIG. 102 , but the total of 64890 bits of the code word having the 64800bits and the adjustment bit string having the 90 bits may be arranged inany order.

Modification of Third Exemplary Embodiment

In the third exemplary embodiment, the configuration of the modulatorthat performs the pieces of processing before mapper 9702 in FIGS. 97and 98 is similar to that in FIG. 73 . One of the characteristics of thethird exemplary embodiment is that

“In order that the number of bits (X+Y) that can be transmitted by firstand second complex signals s1 and s2 transmitted at the identicalfrequency and the identical time does not include the data of theplurality of blocks (of the error correction code) with respect to theset of the complex signals based on any combination of the modulationschemes used in mapper 504 irrespective of the value of N when encoder502LA in FIG. 73 outputs the code word having code word length (blocklength (code length)) N of the error correction code, bit string 503V isinput to bit length adjuster 7301, the adjustment bit string is added tothe front end, the rear end, the predetermined position, and the like ofthe code word of the error correction code having the code word length(block length (code length)) N, and the bit-length-adjusted bit stringfor the mapper is output such that the number of constituting bits isthe multiple of the number of bits (X+Y). The adjustment bit string isconstructed by repeating the bit value in a predetermined portion of theN-bit code word obtained through the coding processing at least once(repetition), or constructed with the predetermined bit string”.The value of (X+Y) is similar to that of the first to third exemplaryembodiments.

In a modulation of the third exemplary embodiment in the tenth exemplaryembodiment, the number of bits of the adjustment bit string is decidedin consideration of change period z of θ(i). The description willspecifically be made below.

A more specific example will be described for convenience.

The error correction code used is set to the code length (block length)of 64800 bits, and change period z of θ(i) is set to 9. QPSK, 16QAM,64QAM, and 256QAM can be used as the modulation scheme. Accordingly,sets of (QPSK,QPSK), (QPSK,16QAM), (QPSK,64QAM), (QPSK,256QAM),(16QAM,16QAM), (16QAM,64QAM), (16QAM,256QAM), (64QAM,256QAM), and(256QAM,256QAM) can be considered as (modulation scheme of s₁(t) (firstcomplex signal s1), modulation scheme of s₂(t) (second complex signals2)), and some examples will be picked up and described below.

In the tenth exemplary embodiment, similarly to other exemplaryembodiments, it is assumed that both the modulation scheme of firstcomplex signal s1 (s₁(t)) and the modulation scheme of the secondcomplex signal s2 (s₂(t)) can be switched from the plurality ofmodulation schemes.

One of the characteristics of the modulation of the third exemplaryembodiment in the tenth exemplary embodiment is that, assuming thatγ=LCM(X+Y,z) is given for the sum of the value of (X+Y), change period zof θ(i), the number of bits (N) of the code length, and the number ofbits of the adjustment bit string, a sum of the number of bits (N) ofthe code length and the number of bits of the adjustment bit string is amultiple of γ. That is, the sum of the number of bits (N) of the codelength and the number of bits of the adjustment bit string is themultiple of the least common multiple of (X+Y) and z, where X is aninteger of 1 or more, Y is an integer of 1 or more, and z is an integerof 2 or more. Accordingly, (X+Y) is an integer of 2 or more. Although itis ideal that the number of bits of the adjustment bit string is 0, andsometimes the number of bits of the adjustment bit string cannot be setto 0. At this point, it is necessary to add the adjustment bit string.

This point will be described below with an example.

Example 5

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(16QAM,16QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(8,9)=72 is obtained. Accordingly, the number ofbits of the adjustment bit string necessary to satisfy the abovecharacteristic is (72×n) bits (n is an integer of 0 or more).

FIG. 101A illustrates the state of first bit string 503Λ that is outputfrom encoder 502LA of the modulator in FIG. 73 . In FIG. 101A, referencemark 10101 designates the ith-block code word in which the number ofbits is 64800, reference mark 10102 designates the (i+1)th-block codeword in which the number of bits is 64800, reference mark 10103designates the (i+2)th-block code word in which the number of bits is64800, reference mark 10104 designates the (i+3)th-block code word inwhich the number of bits is 64800, and the (i+4)th-block code word, the(i+5)th-block code word, and . . . are arranged.

As described above, the number of bits of the adjustment bit stringnecessary to satisfy the above characteristic is (72×n) bits (n is aninteger of 0 or more).

In this case, the number of bits of the adjustment bit string is set to0 (zero). FIG. 101B illustrates the state of bit-length-adjusted bitstring 7303 that is output from bit length adjuster 7301 of themodulator in FIG. 73 . In FIG. 101B, similarly to the state of first bitstring 503Λ output from encoder 502LA in FIG. 73 , inbit-length-adjusted bit string 7303 output from bit length adjuster 7301of the modulator in FIG. 73 , reference mark 10101 designates theith-block code word in which the number of bits is 64800, reference mark10102 designates the (i+1)th-block code word in which the number of bitsis 64800, reference mark 10103 designates the (i+2)th-block code word inwhich the number of bits is 64800, reference mark 10104 designates the(i+3)th-block code word in which the number of bits is 64800, and(i+4)th-block code word, (i+5)th-block code word, and . . . arearranged.

Example 6

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(64QAM,256QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(14,9)=126 is obtained. Accordingly, the numberof bits of the adjustment bit string necessary to satisfy the abovecharacteristic is (126×n+90) bits (n is an integer of 0 or more).

FIG. 103A illustrates the state of first bit string 503Λ that is outputfrom encoder 502LA of the modulator in FIG. 73 . In FIG. 103A, referencemark 10101 designates the ith-block code word in which the number ofbits is 64800, reference mark 10102 designates the (i+1)th-block codeword in which the number of bits is 64800, and the (i+2)th-block codeword, the (i+3)th-block code word, and . . . are arranged.

As described above, the number of bits of the adjustment bit stringnecessary to satisfy the above characteristic is (126×n+90) bits (n isan integer of 0 or more). In this case, the number of bits of theadjustment bit string is set to 90. FIG. 103B illustrates the state ofbit-length-adjusted bit string 7303 that is output from bit lengthadjuster 7301 of the modulator in FIG. 73 .

In FIG. 103B, reference mark 103 a designates (1) bit of the code word,and reference mark 103 b designates the bit of the adjustment bitstring. Total 10301 of code word 10101 of the ith block and theadjustment bit string for code word 10101 of the ith block is 64890bits. Total 10302 of code word 10102 of the (i+1)th block and theadjustment bit string for code word 10102 of the (i+1)th block is 64890bits.

Therefore, the effect of the third exemplary embodiment can be obtained.The sum of code word 10101 of the ith block having 64800 bits and thenumber of bits of the adjustment bit string is the number of slotsnecessary for the transmission of 64890 bits (in this case, one slotmeans one formed by one symbol of s1 and one symbol of s2), and is anintegral multiple of change period (z=9) of θ(i).

Therefore, in the slot having 64890 bits that is of the sum of code word10101 in the ith block having 64800 bits and the number of bits of theadjustment bit string, the number of occurrences of nine values that canbe taken by θ(i) are equal to one another, so that a possibility ofobtaining the information included in code word 10101 of the ith blockwith high reception quality can be enhanced.

Similarly, the sum of code word 10102 of the (i+1)th block having 64800bits and the number of bits of the adjustment bit string is an integralmultiple of period (z=9) of the change in the number of slots θ(i)necessary for the transmission of 64890 bits. Therefore, in the slothaving 64890 bits that is of the sum of code word 10102 in the (i+1)thblock having 64800 bits and the number of bits of the adjustment bitstring, the number of occurrences of nine values that can be taken byθ(i) are equal to one another, so that a possibility of obtaining theinformation included in code word 10102 of the (i+1)th block with highreception quality can be enhanced.

As described in the third exemplary embodiment, the adjustment bitstring is constructed by repeating the bit value in a predeterminedportion of the N-bit code word obtained through the coding processing atleast once (repetition) or constructed with the predetermined bitstring. The specific method for constructing the adjustment bit stringis described in the third exemplary embodiment.

The adjustment bit string inserting method is not limited to that inFIG. 103 , but the total of 64890 bits of the code word having the 64800bits and the adjustment bit string having the 90 bits may be arranged inany order.

Sometimes the interleaving has the size of (N×z) bits as described inthe third exemplary embodiment. In this case, the followingcharacteristic is given.

“In order that the number of bits (X+Y) that can be transmitted by firstand second complex signals s1 and s2 transmitted at the identicalfrequency and the identical time does not include the data of theplurality of blocks (of the error correction code) with respect to theset of the complex signals based on any combination of the modulationschemes used in mapper 504 irrespective of the value of N when encoder502LA in FIG. 73 outputs the code word having code word length (blocklength (code length)) N of the error correction code, bit lengthadjuster 7301 adds the adjustment bit string to the (N×z) bitsaccumulated in the interleaver, and the total of the (N×z) bits and thenumber of bits of the adjustment bit string is a multiple ofγ=LCM(X+Y,z).”

Modification of Fourth Exemplary Embodiment

In the fourth exemplary embodiment, the configuration of the modulatorthat performs the pieces of processing before mapper 9702 in FIGS. 97and 98 is similar to that in FIGS. 80 and 83 . One of thecharacteristics of the fourth exemplary embodiment is that “In secondbit string (bit-length-adjusted bit string) 8003 in which thetemporarily-inserted adjustment bit string is deleted from code length Nof the code word of the LDPC code in the ith block before the coding,the number of bits of second bit string (bit-length-adjusted bit string)8003 is a multiple of the number of bits (X+Y) decided by the set of thefirst modulation scheme of s1 (t) and the second modulation scheme ofs2(t)”.

The value of (X+Y) is similar to that of the first to third exemplaryembodiments.

In a modulation of the fourth exemplary embodiment in the tenthexemplary embodiment, the number of bits of the adjustment bit string isdecided in consideration of change period z of θ(i). The descriptionwill specifically be made below.

A more specific example will be described for convenience.

The error correction code used is set to the code length (block length)of 64800 bits, and change period z of θ(i) is set to 9. QPSK, 16QAM,64QAM, and 256QAM can be used as the modulation scheme. Accordingly,sets of (QPSK,QPSK), (QPSK,16QAM), (QPSK,64QAM), (QPSK,256QAM),(16QAM,16QAM), (16QAM,64QAM), (16QAM,256QAM), (64QAM,256QAM), and(256QAM,256QAM) can be considered as (modulation scheme of s₁(t) (firstcomplex signal s1), modulation scheme of s₂(t) (second complex signals2)), and some examples will be picked up and described below.

In the tenth exemplary embodiment, similarly to other exemplaryembodiments, it is assumed that both the modulation scheme of firstcomplex signal s1 (s₁(t)) and the modulation scheme of the secondcomplex signal s2 (s₂(t)) can be switched from the plurality ofmodulation schemes.

One of the characteristics of the modulation of the fourth exemplaryembodiment in the tenth exemplary embodiment is that, assuming thatγ=LCM(X+Y,z) is given for the sum of the value of (X+Y), change period zof θ(i), the number of bits (N) of the code length, and the number ofbits of the adjustment bit string, the number of bits of thebit-length-adjusted bit string is a multiple of γ. That is, thebit-length-adjusted bit string is the multiple of the least commonmultiple of (X+Y) and z, where X is an integer of 1 or more, Y is aninteger of 1 or more, and z is an integer of 2 or more. Accordingly,(X+Y) is an integer of 2 or more. Although it is ideal that a differencebetween the number of bits of the bit-length-adjusted bit string and thenumber of bits of the code word is 0, and sometimes the differencecannot be set to 0. At this point, it is necessary to adjust the bitlength as described in the characteristic of the fourth exemplaryembodiment.

This point will be described below with an example.

Example 7

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(16QAM,16QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(8,9)=72 is obtained. Accordingly, the number ofbits of the temporarily-inserted adjustment bit string (knowninformation) necessary to satisfy the above characteristic is (72×n)bits (n is an integer of 0 or more).

FIG. 101A illustrates the state of first bit string 503′ (or 503Λ) thatis output from encoder 502 of the modulator in FIGS. 80 and 83 . In FIG.101A, reference mark 10101 designates the ith-block code word in whichthe number of bits is 64800, reference mark 10102 designates the(i+1)th-block code word in which the number of bits is 64800, referencemark 10103 designates the (i+2)th-block code word in which the number ofbits is 64800, reference mark 10104 designates the (i+3)th-block codeword in which the number of bits is 64800, and the (i+4)th-block codeword, the (i+5)th-block code word, and . . . are arranged. Thetemporarily-inserted adjustment bit string (known information) is notincluded in code words 10101, 10102, 10103, 10104 of the block.

As described above, the number of bits of the temporarily-insertedadjustment bit string (known information) necessary to satisfy the abovecharacteristic is (72×n) bits (n is an integer of 0 or more). At thispoint, it is assumed that the number of bits of the temporarily-insertedadjustment bit string (known information) is set to 0 (zero). FIG. 101Billustrates the state of bit-length-adjusted bit string 8003 that isoutput from subsequent stage section 8001B in FIGS. 80 and 83 . In FIG.101B, similarly to the state of first bit string 503′ (or 503Λ) outputfrom R102 of the modulator in FIGS. 80 and 83 , in bit-length-adjustedbit string 8003 output from subsequent stage section 8001B in FIGS. 80and 83 , reference mark 10101 designates the ith-block code word inwhich the number of bits is 64800, reference mark 10102 designates the(i+1)th-block code word in which the number of bits is 64800, referencemark 10103 designates the (i+2)th-block code word in which the number ofbits is 64800, reference mark 10104 designates the (i+3)th-block codeword in which the number of bits is 64800, and (i+4)th-block code word,(i+5)th-block code word, and . . . are arranged.

Example 8

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(64QAM,256QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(14,9)=126 is obtained. Accordingly, the numberof bits of the temporarily-inserted adjustment bit string (knowninformation) necessary to satisfy the above characteristic is (126×n+36)bits (n is an integer of 0 or more).

FIG. 104A illustrates the state of first bit string 503′ (or 503Λ) thatis output from encoder 502 of the modulator in FIGS. 80 and 83 . In FIG.104A, reference mark 10401 designates the ith-block code word in whichthe number of bits is 64800, reference mark 10402 designates the(i+1)th-block code word in which the number of bits is 64800, and the(i+2)th-block code word, the (i+3)th-block code word, and . . . arearranged.

In FIG. 104 , reference mark 104 b designates the bit of thetemporarily-inserted adjustment bit string, and reference mark 104 adesignates the other bits.

Accordingly, bits 104 b of the temporarily-inserted adjustment bitstring having the 36 bits exist in code word 10401 of FIG. 104A of theith block having the 64800 bits, and bits 104 b of thetemporarily-inserted adjustment bit string having the 36 bits exist incode word 10402 of the (i+1)th block having the 64800 bits.

As described above, the number of bits of the temporarily-insertedadjustment bit string (known information) necessary to satisfy the abovecharacteristic is (126×n+36) bits (n is an integer of 0 or more). Atthis point, it is assumed that the number of bits of thetemporarily-inserted adjustment bit string (known information) is set to36. Subsequent stage section 8001B in FIGS. 80 and 83 deletes thetemporarily-inserted adjustment bit string (known information). FIG.104B illustrates the state of bit-length-adjusted bit string 8003 thatis output from subsequent stage section 8001B of the modulator in FIGS.80 and 83 .

In FIG. 104B, ith bit-length-adjusted bit string 10403 is constructedonly with bits 104 a. The number of bits of ith bit-length-adjusted bitstring 10403 is 64800−36=64764.

Similarly, (i+1)th bit-length-adjusted bit string 10404 is constructedonly with bits 104 a. The number of bits of (i+1)th bit-length-adjustedbit string 10404 is 64800−36=64764.

Therefore, the effect of the fourth exemplary embodiment can beobtained.

The number of slots necessary for the transmission of the ithbit-length-adjusted bit string (in this case, one slot means one formedby one symbol of s₁ and one symbol of s2) is an integral multiple ofchange period (z=9) of θ(i).

Therefore, in the slot forming the ith bit-length-adjusted bit string,the number of occurrences of nine values that can be taken by θ(i) areequal to one another, so that a possibility of obtaining the informationincluded in the ith bit-length-adjusted bit string with high receptionquality can be enhanced.

The number of slots necessary for the transmission of the (i+1)thbit-length-adjusted bit string (in this case, one slot means one formedby one symbol of s1 and one symbol of s2) is an integral multiple ofchange period (z=9) of θ(i).

Therefore, in the slot forming the (i+1)th bit-length-adjusted bitstring, the number of occurrences of nine values that can be taken byθ(i) are equal to one another, so that a possibility of obtaining theinformation included in the (i+1)th bit-length-adjusted bit string withhigh reception quality can be enhanced.

The specific method for constructing the temporarily-inserted adjustmentbit string (known information) is described in the fourth exemplaryembodiment.

Modification of Eighth Exemplary Embodiment

In the eighth exemplary embodiment, the configuration of the modulatorthat performs the pieces of processing before mapper 9702 in FIGS. 97and 98 is similar to that in FIGS. 91 and 93 . One of thecharacteristics of the eighth exemplary embodiment is that “The bitlength adjuster deletes the PunNum-bit data from the N-bit code word,and outputs the (N− PunNum)-bit data string. At this point, PunNum isdecided such that (N− PunNum) is the multiple of the value of (X+Y)”.

The value of (X+Y) is similar to that of the first to third exemplaryembodiments.

In a modulation of the eighth exemplary embodiment in the tenthexemplary embodiment, the number of bits PunNum of the deleted data isdecided in consideration of change period z of θ(i). The descriptionwill specifically be made below.

A more specific example will be described for convenience.

The error correction code used is set to the code length (block length)of 64800 bits, and change period z of θ(i) is set to 9. QPSK, 16QAM,64QAM, and 256QAM can be used as the modulation scheme. Accordingly,sets of (QPSK,QPSK), (QPSK,16QAM), (QPSK,64QAM), (QPSK,256QAM),(16QAM,16QAM), (16QAM,64QAM), (16QAM,256QAM), (64QAM,256QAM), and(256QAM,256QAM) can be considered as (modulation scheme of s₁(t) (firstcomplex signal s1), modulation scheme of s₂(t) (second complex signals2)), and some examples will be picked up and described below.

In the tenth exemplary embodiment, similarly to other exemplaryembodiments, it is assumed that both the modulation scheme of firstcomplex signal s1 (s₁(t)) and the modulation scheme of the secondcomplex signal s2 (s₂(t)) can be switched from the plurality ofmodulation schemes.

One of the characteristics of the modulation of the eighth exemplaryembodiment in the tenth exemplary embodiment is that, assuming thatγ=LCM(X+Y,z) is given for the sum of the value of (X+Y), change period zof θ(i), the number of bits (N) of the code length, and the number ofbits of the adjustment bit string, the number of bits (N− PunNum) of the(N− PunNum)-bit data string is a multiple of γ. That is, (N− PunNum) isthe multiple of the least common multiple of (X+Y) and z, where X is aninteger of 1 or more, Y is an integer of 1 or more, and z is an integerof 2 or more. Accordingly, (X+Y) is an integer of 2 or more. Although itis ideal that PunNum is 0, and sometimes PunNum cannot be set to 0. Atthis point, it is necessary to adjust (N− PunNum) as described in thecharacteristic of the eighth exemplary embodiment.

This point will be described below with an example.

Example 9

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(16QAM,16QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(8,9)=72 is obtained. Accordingly, PunNumnecessary to satisfy the above characteristic is (72×n) bits (n is aninteger of 0 or more).

FIG. 101A illustrates the state of N-bit code word 503 that is outputfrom encoder 502 of the modulator in FIGS. 91 and 93 . In FIG. 101A,reference mark 10101 designates the ith-block code word in which thenumber of bits is 64800, reference mark 10102 designates the(i+1)th-block code word in which the number of bits is 64800, referencemark 10103 designates the (i+2)th-block code word in which the number ofbits is 64800, reference mark 10104 designates the (i+3)th-block codeword in which the number of bits is 64800, and the (i+4)th-block codeword, the (i+5)th-block code word, and . . . are arranged.

As described above, PunNum necessary to satisfy the above characteristicis (72×n) bits (n is an integer of 0 or more). At this point, PunNum isset to 0 (zero). FIG. 101B illustrates the state of (N− PunNum)-bit datastring 9102 that is output from bit length adjuster 9101 in FIGS. 91 and93 . In FIG. 101B, similarly to the state of first bit string 503′ (or503Λ) output from encoder 502 in FIGS. 91 and 93 , in (N− PunNum)-bitdata string 9102 output from bit length adjuster 9101, reference mark10101 designates the ith-block code word in which the number of bits is64800, reference mark 10102 designates the (i+1)th-block code word inwhich the number of bits is 64800, reference mark 10103 designates the(i+2)th-block code word in which the number of bits is 64800, referencemark 10104 designates the (i+3)th-block code word in which the number ofbits is 64800, and (i+4)th-block code word, (i+5)th-block code word, and. . . are arranged.

Example 10

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(64QAM,256QAM), that the error correction code (for example, the blockcode of the LDPC code) has the code word length (block length (codelength)) of 64800 bits, and that change period z of θ(i) is set to 9.Therefore, γ=LCM(X+Y,z)=(14,9)=126 is obtained. Accordingly, PunNumnecessary to satisfy the above characteristic is (126×n+36) bits (n isan integer of 0 or more).

FIG. 105A illustrates the state of N-bit code word 503 that is outputfrom encoder 502 of the modulator in FIGS. 91 and 93 . In FIG. 105A,reference mark 10101 designates the ith-block code word in which thenumber of bits is 64800, reference mark 10102 designates the(i+1)th-block code word in which the number of bits is 64800, referencemark 10103 designates the (i+2)th-block code word in which the number ofbits is 64800, reference mark 10104 designates the (i+3)th-block codeword in which the number of bits is 64800, and the (i+4)th-block codeword, the (i+5)th-block code word, and . . . are arranged.

As described above, PunNum necessary to satisfy the above characteristicis (126×n+36) bits (n is an integer of 0 or more). In this case, PunNumis set to 36 bits. FIG. 105B illustrates the state of (N-PunNum)-bitdata string 9102 that is output from bit length adjuster 9101 in FIGS.91 and 93 .

In FIG. 105B, ith bit-length-adjusted bit string 10501 is the ith datastring having (N− PunNum) bits. Accordingly, ith bit-length-adjusted bitstring 10501 is constructed with (64800−36=64764) bits.

Similarly, (i+1)th bit-length-adjusted bit string 10502 is the (i+1)thdata string having (N− PunNum) bits. Accordingly, (i+1)thbit-length-adjusted bit string 10502 is constructed with(64800-36=64764) bits, (i+2)th bit-length-adjusted bit string 10503 isthe (i+2)th data string having (N− PunNum) bits. Accordingly, (i+2)thbit-length-adjusted bit string 10503 is constructed with(64800−36=64764) bits.

(i+3)th bit-length-adjusted bit string 10504 is the (i+3)th data stringhaving (N− PunNum) bits. Accordingly, (i+3)th bit-length-adjusted bitstring 10504 is constructed with (64800−36=64764) bits. Therefore, theeffect of the eighth exemplary embodiment can be obtained.

The number of slots necessary for the transmission of the ithbit-length-adjusted block (in this case, one slot means one formed byone symbol of s1 and one symbol of s2) is an integral multiple of changeperiod (z=9) of θ(i).

Therefore, in the slot forming the ith bit-length-adjusted block, thenumber of occurrences of nine values that can be taken by θ(i) are equalto one another, so that a possibility of obtaining the informationincluded in the ith bit-length-adjusted block with high receptionquality can be enhanced.

The number of slots necessary for the transmission of the (i+1)thbit-length-adjusted block (in this case, one slot means one formed byone symbol of s1 and one symbol of s2) is an integral multiple of changeperiod (z=9) of θ(i).

Therefore, in the slot forming the (i+1)th bit-length-adjusted block,the number of occurrences of nine values that can be taken by θ(i) areequal to one another, so that a possibility of obtaining the informationincluded in the (i+1)th bit-length-adjusted block with high receptionquality can be enhanced.

The number of slots necessary for the transmission of the (i+2)thbit-length-adjusted block (in this case, one slot means one formed byone symbol of s1 and one symbol of s2) is an integral multiple of changeperiod (z=9) of θ(i).

Therefore, in the slot forming the (i+2)th bit-length-adjusted block,the number of occurrences of nine values that can be taken by θ(i) areequal to one another, so that a possibility of obtaining the informationincluded in the (i+2)th bit-length-adjusted block with high receptionquality can be enhanced.

The number of slots necessary for the transmission of the (i+3)thbit-length-adjusted block (in this case, one slot means one formed byone symbol of s1 and one symbol of s2) is an integral multiple of changeperiod (z=9) of θ(i).

Therefore, in the slot forming the (i+3)th bit-length-adjusted block,the number of occurrences of nine values that can be taken by θ(i) areequal to one another, so that a possibility of obtaining the informationincluded in the (i+3)th bit-length-adjusted block with high receptionquality can be enhanced.

The same holds true for the subsequent bit-length-adjusted block.

The receiver can obtain the data having the high reception quality byperforming the above examples. The configuration of the receiver issimilar to that of the fifth to eighth exemplary embodiments (however,the bit length adjusting method is described in the tenth exemplaryembodiment).

When the bit-length-adjusted block satisfied one of the above exampleswith respect to the set of the complex signals based on any combinationof the modulation schemes (s1 and s2) irrespective of the value of Nwhile the encoder outputs the code word code word having the N-bit codeword length (block length (code length)) of the error correction code,there is a high possibility of effectively reducing the memory of thetransmitter and/or receiver.

Eleventh Exemplary Embodiment

In the first to tenth exemplary embodiments, the method in which thecontrol is performed such that “the bit-length-adjusted block is themultiple of the value of (X+Y) when the encoder outputs the code wordhaving the N-bit code word length (block length (code length)) of theerror correction code” is described using the plurality of examples.“The bit-length-adjusted block is the multiple of the value of (X+Y)when the encoder outputs the code word having the N-bit code word length(block length (code length)) of the error correction code” will bedescribed again in an eleventh exemplary embodiment.

The value of (X+Y) is similar to that of the first to third exemplaryembodiments.

In the eleventh exemplary embodiment, the code length (block length) ofthe error correction code is set to 16200 bits or 64800 bits, and setsof (QPSK,QPSK), (QPSK,16QAM), (QPSK,64QAM), (QPSK,256QAM),(16QAM,16QAM), (16QAM,64QAM), (16QAM,256QAM), (64QAM,256QAM), and(256QAM,256QAM) are considered as (modulation scheme of s₁(t) (firstcomplex signal s1), modulation scheme of s₂(t) (second complex signals2)) (hereinafter, n is an integer of 0 or more).

From the above, the following are given.

[1]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,QPSK), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 4).

[1-1] The number of bits of the adjustment bit string (to be added) is(4×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[1-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (4×n) when the method of the fourthexemplary embodiment is adopted (where 4×n<16200).

[1-3] The number of bits of PunNum (the bits to be deleted) is (4×n)when the method of the eighth exemplary embodiment is adopted (where4×n<16200).

[2]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,16QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 6).

[2-1] The number of bits of the adjustment bit string (to be added) is(6×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[2-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (6×n) when the method of the fourthexemplary embodiment is adopted (where 6×n<16200).

[2-3] The number of bits of PunNum (the bits to be deleted) is (6×n)when the method of the eighth exemplary embodiment is adopted (where6×n<16200).

[3]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,64QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 8).

[3-1] The number of bits of the adjustment bit string (to be added) is(8×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[3-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (8×n) when the method of the fourthexemplary embodiment is adopted (where 8×n<16200).

[3-3] The number of bits of PunNum (the bits to be deleted) is (8×n)when the method of the eighth exemplary embodiment is adopted (where8×n<16200).

[4]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,256QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 10).

[4-1] The number of bits of the adjustment bit string (to be added) is(10×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[4-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (10×n) when the method of the fourthexemplary embodiment is adopted (where 10×n<16200).

[4-3] The number of bits of PunNum (the bits to be deleted) is (10×n)when the method of the eighth exemplary embodiment is adopted (where10×n<16200).

[5]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,16QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 8).

[5-1] The number of bits of the adjustment bit string (to be added) is(8×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[5-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (8×n) when the method of the fourthexemplary embodiment is adopted (where 8×n<16200).

[5-3] The number of bits of PunNum (the bits to be deleted) is (8×n)when the method of the eighth exemplary embodiment is adopted (where8×n<16200).

[6]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,64QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 10).

[6-1] The number of bits of the adjustment bit string (to be added) is(10×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[6-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (10×n) when the method of the fourthexemplary embodiment is adopted (where 10×n<16200).

[6-3] The number of bits of PunNum (the bits to be deleted) is (10×n)when the method of the eighth exemplary embodiment is adopted (where10×n<16200).

[7]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 12).

[7-1] The number of bits of the adjustment bit string (to be added) is(12×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[7-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (12×n) when the method of the fourthexemplary embodiment is adopted (where 12×n<16200).

[7-3] The number of bits of PunNum (the bits to be deleted) is (12×n)when the method of the eighth exemplary embodiment is adopted (where12×n<16200).

[8]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(64QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 14).

[8-1] The number of bits of the adjustment bit string (to be added) is(14×n+12) when one of the methods of the first to third exemplaryembodiments is adopted.

[8-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (14×n+2) when the method of the fourthexemplary embodiment is adopted (where 14×n+2<16200).

[8-3] The number of bits of PunNum (the bits to be deleted) is (14×n+2)when the method of the eighth exemplary embodiment is adopted (where14×n+2<16200).

[9]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(256QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 16).

[9-1] The number of bits of the adjustment bit string (to be added) is(16×n+8) when one of the methods of the first to third exemplaryembodiments is adopted.

[9-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (16×n+8) when the method of the fourthexemplary embodiment is adopted (where 16×n+8<16200).

[9-3] The number of bits of PunNum (the bits to be deleted) is (16×n+8)when the method of the eighth exemplary embodiment is adopted (where16×n+8<16200).

[10]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,QPSK), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 4).

[10-1] The number of bits of the adjustment bit string (to be added) is(4×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[10-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (4×n) when the method of the fourthexemplary embodiment is adopted (where 4×n<64800).

[10-3] The number of bits of PunNum (the bits to be deleted) is (4×n)when the method of the eighth exemplary embodiment is adopted (where4×n<64800).

[11]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,16QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 6).

[11-1] The number of bits of the adjustment bit string (to be added) is(6×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[11-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (6×n) when the method of the fourthexemplary embodiment is adopted (where 6×n<64800).

[11-3] The number of bits of PunNum (the bits to be deleted) is (6×n)when the method of the eighth exemplary embodiment is adopted (where6×n<64800).

[12]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,64QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 8).

[12-1] The number of bits of the adjustment bit string (to be added) is(8×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[12-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (8×n) when the method of the fourthexemplary embodiment is adopted (where 8×n<64800).

[12-3] The number of bits of PunNum (the bits to be deleted) is (8×n)when the method of the eighth exemplary embodiment is adopted (where8×n<64800).

[13]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,256QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 10).

[13-1] The number of bits of the adjustment bit string (to be added) is(10×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[13-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (10×n) when the method of the fourthexemplary embodiment is adopted (where 10×n<64800).

[13-3] The number of bits of PunNum (the bits to be deleted) is (10×n)when the method of the eighth exemplary embodiment is adopted (where10×n<64800).

[14]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,16QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 8). [14-1]The number of bits of the adjustment bit string (to be added) is (8×n)when one of the methods of the first to third exemplary embodiments isadopted. [14-2] The number of bits of the temporarily-insertedadjustment bit string (known information) is (8×n) when the method ofthe fourth exemplary embodiment is adopted (where 8×n<64800). [14-3] Thenumber of bits of PunNum (the bits to be deleted) is (8×n) when themethod of the eighth exemplary embodiment is adopted (where 8×n<64800).

[15]

It is assumed that (modulation scheme of s₁(t) (first complex signals₁), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,64QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 10).

[15-1] The number of bits of the adjustment bit string (to be added) is(10×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[15-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (10×n) when the method of the fourthexemplary embodiment is adopted (where 10×n<64800).

[15-3] The number of bits of PunNum (the bits to be deleted) is (10×n)when the method of the eighth exemplary embodiment is adopted (where10×n<64800).

[16]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 12).

[16-1] The number of bits of the adjustment bit string (to be added) is(12×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[16-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (12×n) when the method of the fourthexemplary embodiment is adopted (where 12>n<64800).

[16-3] The number of bits of PunNum (the bits to be deleted) is (12×n)when the method of the eighth exemplary embodiment is adopted (where12×n<64800).

[17]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(64QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 14).

[17-1] The number of bits of the adjustment bit string (to be added) is(14×n+6) when one of the methods of the first to third exemplaryembodiments is adopted.

[17-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (14×n+8) when the method of the fourthexemplary embodiment is adopted (where 14×n+8<64800).

[17-3] The number of bits of PunNum (the bits to be deleted) is (14×n+8)when the method of the eighth exemplary embodiment is adopted (where14×n+8<64800).

[18]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(256QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 16).

[18-1] The number of bits of the adjustment bit string (to be added) is(16×n) when one of the methods of the first to third exemplaryembodiments is adopted.

[18-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (16×n) when the method of the fourthexemplary embodiment is adopted (where 16×n<64800).

[18-3] The number of bits of PunNum (the bits to be deleted) is (16×n)when the method of the eighth exemplary embodiment is adopted (where16×n<64800).

For example, the communication system can set one of the modulationscheme sets of (QPSK,QPSK), (QPSK,16QAM), (QPSK,64QAM), (QPSK,256QAM),(16QAM,16QAM), (16QAM,64QAM), (16QAM,256QAM), (64QAM,256QAM), and(256QAM,256QAM) as (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)), and set thecode length (block length) of the error correction code to one of 16200bits and 64800 bits.

At this point, it is necessary to satisfy one of the conditionsdescribed in [1] to [18], One of the characteristics is that, even if(modulation scheme of s₁(t) (first complex signal s1), modulation schemeof s₂(t) (second complex signal s2)) is a certain modulation scheme set,the number of bits to be added or the number of bits to be deletedvaries depending on the code length (block length) of the errorcorrection code.

Case 1 and Case 2 are cited as a specific example.

Case 1:

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(64QAM,256QAM). It is assumed that the transmitter can set the codelength (block length) of the error correction code to one of the 16200bits and the 64800 bits.

When the transmitter selects the 16200 bits as the code length (blocklength) of the error correction code, for example, the number of bits ofthe adjustment bit string (to be added) is set to 12 in applying [8-1],the number of bits of the temporarily-inserted adjustment bit string(known information) is set to 2 in applying [8-2], and the number ofbits of PunNum (to be deleted) is set to 2 in applying [8-3],

When the transmitter selects the 64800 bits as the code length (blocklength) of the error correction code, for example, the number of bits ofthe adjustment bit string (to be added) is set to 6 in applying [17-1],the number of bits of the temporarily-inserted adjustment bit string(known information) is set to 8 in applying [17-2], and the number ofbits of PunNum (to be deleted) is set to 8 in applying [17-3],

Case 2:

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(256QAM,256QAM). It is assumed that the transmitter can set the codelength (block length) of the error correction code to one of the 16200bits and the 64800 bits.

When the transmitter selects the 16200 bits as the code length (blocklength) of the error correction code, for example, the number of bits ofthe adjustment bit string (to be added) is set to 8 in applying [9-1],the number of bits of the temporarily-inserted adjustment bit string(known information) is set to 8 in applying [9-2], and the number ofbits of PunNum (to be deleted) is set to 8 in applying [9-3],

When the transmitter selects the 64800 bits as the code length (blocklength) of the error correction code, for example, the number of bits ofthe adjustment bit string (to be added) is set to 0 in applying [18-1],the number of bits of the temporarily-inserted adjustment bit string(known information) is set to 0 in applying [18-2], and the number ofbits of PunNum (to be deleted) is set to 0 in applying [18-3],

Then, the code length (block length) of the error correction code is setto 16200 bits or 64800 bits, sets of (QPSK,QPSK), (QPSK,16QAM),(QPSK,64QAM), (QPSK,256QAM), (16QAM,16QAM), (16QAM,64QAM),(16QAM,256QAM), (64QAM,256QAM), and (256QAM,256QAM) are considered as(modulation scheme of s₁(t) (first complex signal s1), modulation schemeof s₂(t) (second complex signal s2)), and it is considered that themethod of the tenth exemplary embodiment is adopted. However, changeperiod z of 0(i) of the tenth exemplary embodiment is set to 9(hereinafter, n is an integer of 0 or more).

From the above, the following are given.

[19]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,QPSK), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 4).

[19-1] The number of bits of the adjustment bit string (to be added) is(36×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[19-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (36×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 36×n<16200)

[19-3] The number of bits of PunNum (the bits to be deleted) is (36×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 36×n<216200).

[20]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,16QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 6).

[20-1] The number of bits of the adjustment bit string (to be added) is(18×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[20-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (18×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 18×n<16200)

[20-3] The number of bits of PunNum (the bits to be deleted) is (18×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 18×n<16200).

[21]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,64QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 8).

[21-1] The number of bits of the adjustment bit string (to be added) is(72×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[21-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (72×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 72×n<16200).

[21-3] The number of bits of PunNum (the bits to be deleted) is (72×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 72×n<16200).

[22]

It is assumed that (modulation scheme of s₁(t) (first complex signals₁), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,256QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 10).

[22-1] The number of bits of the adjustment bit string (to be added) is(90×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[22-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (90×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 90×n<16200).

[22-3] The number of bits of PunNum (the bits to be deleted) is (90×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 90×n<16200).

[23]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,16QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 8).

[23-1] The number of bits of the adjustment bit string (to be added) is(72×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[23-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (72×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 72×n<16200).

[23-3] The number of bits of PunNum (the bits to be deleted) is (72×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 72×n<16200).

[24]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,64QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 10).

[24-1] The number of bits of the adjustment bit string (to be added) is(90×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[24-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (90×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 90×n<16200).

[24-3] The number of bits of PunNum (the bits to be deleted) is (90×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 90×n<16200).

[25]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 12).

[25-1] The number of bits of the adjustment bit string (to be added) is(36×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[25-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (36×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 36×n<16200).

[25-3] The number of bits of PunNum (the bits to be deleted) is (36×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 36×n<16200).

[26]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(64QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 14).

[26-1] The number of bits of the adjustment bit string (to be added) is(126×n+54) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[26-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (126×n+72) when the method of themodification of the fourth exemplary embodiment in the tenth exemplaryembodiment is adopted (where 126×n+72<16200).

[26-3] The number of bits of PunNum (the bits to be deleted) is(126×n+72) when the method of the modification of the eighth exemplaryembodiment in the tenth exemplary embodiment is adopted (where126×n+72<16200).

[27]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(256QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 16200 bits (the value of (X+Y) is 16).

[27-1] The number of bits of the adjustment bit string (to be added) is(144×n+72) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[27-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (144×n+72) when the method of themodification of the fourth exemplary embodiment in the tenth exemplaryembodiment is adopted (where 144×n+72<16200).

[27-3] The number of bits of PunNum (the bits to be deleted) is(144×n+72) when the method of the modification of the eighth exemplaryembodiment in the tenth exemplary embodiment is adopted (where144×n+72<16200).

[28]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,QPSK), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 4).

[28-1] The number of bits of the adjustment bit string (to be added) is(36×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[28-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (36×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 36×n<64800).

[28-3] The number of bits of PunNum (the bits to be deleted) is (36×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 36×n<64800).

[29]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,16QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 6).

[29-1] The number of bits of the adjustment bit string (to be added) is(18×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[29-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (18×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 18×n<64800).

[29-3] The number of bits of PunNum (the bits to be deleted) is (18×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 18×n<64800).

[30]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,64QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 8).

[30-1] The number of bits of the adjustment bit string (to be added) is(72×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[30-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (72×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 72×n<64800).

[30-3] The number of bits of PunNum (the bits to be deleted) is (72×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 72×n<64800).

[31]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(QPSK,256QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 10).

[31-1] The number of bits of the adjustment bit string (to be added) is(90×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[31-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (90×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 90×n<64800). [31-3] The number of bits of PunNum (thebits to be deleted) is (90×n) when the method of the modification of theeighth exemplary embodiment in the tenth exemplary embodiment is adopted(where 90×n<64800).

[32]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,16QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 8).

[32-1] The number of bits of the adjustment bit string (to be added) is(72×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[32-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (72×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 72×n<64800).

[32-3] The number of bits of PunNum (the bits to be deleted) is (72×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 72×n<64800).

[33]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,64QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 10).

[33-1] The number of bits of the adjustment bit string (to be added) is(90×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[33-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (90×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 90×n<64800).

[33-3] The number of bits of PunNum (the bits to be deleted) is (90×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 90×n<64800).

[34]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(16QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 12).

[34-1] The number of bits of the adjustment bit string (to be added) is(36×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[34-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (36×n) when the method of the modificationof the fourth exemplary embodiment in the tenth exemplary embodiment isadopted (where 36×n<64800).

[34-3] The number of bits of PunNum (the bits to be deleted) is (36×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 36×n<64800).

[35]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(64QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 14).

[35-1] The number of bits of the adjustment bit string (to be added) is(126×n+90) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[35-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (126×n+36) when the method of themodification of the fourth exemplary embodiment in the tenth exemplaryembodiment is adopted (where 126×n+36<64800).

[35-3] The number of bits of PunNum (the bits to be deleted) is(126×n+36) when the method of the modification of the eighth exemplaryembodiment in the tenth exemplary embodiment is adopted (where126×n+36<64800).

[36]

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is set to(256QAM,256QAM), and that the code length (block length) of the errorcorrection code is set to 64800 bits (the value of (X+Y) is 16).

[36-1] The number of bits of the adjustment bit string (to be added) is(144×n) when one of the methods of the modifications of the first tothird exemplary embodiments in the tenth exemplary embodiment isadopted.

[36-2] The number of bits of the temporarily-inserted adjustment bitstring (known information) is (144×n) when the method of themodification of the fourth exemplary embodiment in the tenth exemplaryembodiment is adopted (where 144×n<64800).

[36-3] The number of bits of PunNum (the bits to be deleted) is (144×n)when the method of the modification of the eighth exemplary embodimentin the tenth exemplary embodiment is adopted (where 144×n<64800).

For example, the communication system can set one of the modulationscheme sets of (QPSK,QPSK), (QPSK,16QAM), (QPSK,64QAM), (QPSK,256QAM),(16QAM,16QAM), (16QAM,64QAM), (16QAM,256QAM), (64QAM,256QAM), and(256QAM,256QAM) as (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)), and set thecode length (block length) of the error correction code to one of 16200bits and 64800 bits. However, change period z of θ(i) in the tenthexemplary embodiment is set to 9.

At this point, it is necessary to satisfy one of the conditionsdescribed in [19] to [36], One of the characteristics is that, even if(modulation scheme of s₁(t) (first complex signal s1), modulation schemeof s₂(t) (second complex signal s2)) is a certain modulation scheme set,the number of bits to be added or the number of bits to be deletedvaries depending on the code length (block length) of the errorcorrection code.

Case 3 and Case 4 are cited as a specific example.

Case 3:

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(64QAM,256QAM). It is assumed that the transmitter can set the codelength (block length) of the error correction code to one of the 16200bits and the 64800 bits.

When the transmitter selects the 16200 bits as the code length (blocklength) of the error correction code, for example, the number of bits ofthe adjustment bit string (to be added) is set to 54 in applying [26-1],the number of bits of the temporarily-inserted adjustment bit string(known information) is set to 72 in applying [26-2], and the number ofbits of PunNum (to be deleted) is set to 72 in applying [26-3],

When the transmitter selects the 64800 bits as the code length (blocklength) of the error correction code, for example, the number of bits ofthe adjustment bit string (to be added) is set to 90 in applying [35-1],the number of bits of the temporarily-inserted adjustment bit string(known information) is set to 36 in applying [35-2], and the number ofbits of PunNum (to be deleted) is set to 36 in applying [35-3],

Case 4:

It is assumed that (modulation scheme of s₁(t) (first complex signals1), modulation scheme of s₂(t) (second complex signal s2)) is(256QAM,256QAM). It is assumed that the transmitter can set the codelength (block length) of the error correction code to one of the 16200bits and the 64800 bits.

When the transmitter selects the 16200 bits as the code length (blocklength) of the error correction code, for example, the number of bits ofthe adjustment bit string (to be added) is set to 72 in applying [27-1],the number of bits of the temporarily-inserted adjustment bit string(known information) is set to 72 in applying [27-2], and the number ofbits of PunNum (to be deleted) is set to 72 in applying [27-3],

When the transmitter selects the 64800 bits as the code length (blocklength) of the error correction code, for example, the number of bits ofthe adjustment bit string (to be added) is set to 0 in applying [36-1],the number of bits of the temporarily-inserted adjustment bit string(known information) is set to 0 in applying [36-2], and the number ofbits of PunNum (to be deleted) is set to 0 in applying [36-3],

Twelfth Exemplary Embodiment

A method for applying the bit length adjusting methods of the first toeleventh exemplary embodiments to a DVB standard will be described in atwelfth exemplary embodiment.

The case that the method is applied to a broadcasting system in which aDVB (Digital Video Broadcasting)—T2 (T: Terrestrial) standard is usedwill be described below. First, a frame configuration of thebroadcasting system in which the DVB-T2 standard is used will bedescribed.

FIG. 106 illustrates an outline of the frame configuration of the signaltransmitted from the broadcasting station in the DVB-T2 standard. In theDVB-T2 standard, the frame is constructed on the time-frequency axisbecause of the use of the OFDM scheme. FIG. 106 illustrates the frameconfiguration on the time-frequency axis, the frame is constructed withP1 signalling data (hereinafter, sometimes referred to as a P1 symbol)(10601), L1 pre-signalling data (10602), L1 post-signalling data(10603), common PLP (10604), and PLPs (Physical Layer Pipes) #1 to #N(10605_1 to 10605_N) (hereinafter, L1 pre-signalling data (10602) and L1post-signalling data (10603) are referred to as P2 symbol). The frameconstructed with P1 signalling data (10601), L1 pre-signalling data(10602), L1 post-signalling data (10603), common PLP (10604), and PLPs#1 to #N (10605_1 to 10605_N) is referred to as a T2 frame, and is aunit of the frame configuration.

P1 signalling data (10601) transmits information, which indicates asymbol for performing the signal detection and frequency synchronization(including frequency offset estimation) with the receiver, about an FFT(Fast Fourier Transform) size in the frame, and also transmitsinformation indicating which one of an SISO (Single-Input Single-Output)scheme and an MISO (Multiple-Input Single-Output) scheme is used totransmit the modulated signal (in the DVB-T2 standard, one modulatedsignal is transmitted by the SISO scheme, a plurality of modulatedsignals are transmitted by the MISO scheme, and the time-space blockcode described in NPLs 5, 7, and 8 is used).

In the twelfth exemplary embodiment, a plurality of modulated signalsmay be generated for the SISO scheme, and transmitted from a pluralityof antennas.

L1 pre-signalling data (10602) transmits information about a guardinterval used in a transmission frame, information about a signalprocessing method for reducing a PAPR (Peak to Average Power Ratio), amodulation scheme used to transmit the L1 post-signalling data, FEC(Forward Error Correction), information about a coding rate of the FEC,information about a size of the L1 post-signalling data and informationsize, information about a pilot pattern, information about a cell(frequency region) unique number, and information indicating which oneof a normal mode and an extension mode (the normal mode and theextension mode differ from each other in the number of sub-carriers usedin the data transmission) is used.

L1 post-signalling data (10603) transmits information about the numberof PLPs, information about the frequency region to be used, informationabout the unique number of each PLP, the modulation scheme used totransmit each PLP, the EFC, the information about the coding rate of theFEC, and information about the number of blocks transmitted using eachPLP.

Common PLP (10604) and PLPs #1 to #N (10605_1 to 10605_N) are a regionwhere the data is transmitted.

In the frame configuration of FIG. 106 , P1 signalling data (10601), L1pre-signalling data (10602), L1 post-signalling data (10603), common PLP(10604), and PLPs #1 to #N (10605_1 to 10605_N) are transmitted in atime-division manner. However, actually at least two kinds of signalsexist at the identical clock time. FIG. 107 illustrates an example ofthe case that at least two kinds of the signals exist at the identicalclock time. As illustrated in FIG. 107 , sometimes the L1 pre-signallingdata, the L1 post-signalling data, and the common PLP exist at theidentical clock time or PLPs #1 and #2 exist at the identical clocktime. That is, the frame is constructed while each signal is transmittedin both the time division manner and the frequency-division manner.

FIG. 108 illustrates an example of the configuration of the transmitterto which the transmission method in which the precoding and the phasechange are performed is applied (for example, in the broadcastingstation) pursuant to the DVB-T2 standard.

PLP transmission data 10801 (data for the plurality of PLPs) and controlsignal 10809 are input to PLP signal generator 10802, and PLP signalgenerator 10802 performs the error correction coding based oninformation about the error correction coding of each PLP included incontrol signal 10809 and information about the modulation scheme,performs the mapping based on the modulation scheme, and outputs PLP(quadrature) baseband signal 10803.

P2 symbol transmission data 10804 and control signal 10809 are input toP2 symbol signal generator 10805, and P2 symbol signal generator 10805performs the error correction coding based on information about theerror correction coding of the P2 symbol and the information about themodulation scheme, which are included in control signal 10809, performsthe mapping based on the modulation scheme, and outputs P2 symbol(quadrature) baseband signal 10806.

P1 symbol transmission data 10807 and P2 symbol transmission data 10804are input to control signal generator 10808, and control signalgenerator 10808 outputs information about the method (the errorcorrection code, the coding rate of the error correction code, themodulation scheme, the block length, the frame configuration, theselected transmission method including the transmission method in whichthe precoding matrix is regularly switched, the pilot symbol insertingmethod, the information about the IFFT (Inverse Fast FourierTransform)/FFT, the information about the PAPR reducing method, and theinformation about the guard interval inserting method) for transmittingeach symbol group (P1 signalling data (10601), L1 pre-signalling data(10602), L1 post-signalling data (10603), common PLP (10604), and PLPs#1 to #N (10605_1 to 10605_N)) in FIG. 106 as control signal 10809.

PLP baseband signal 10812, P2 symbol baseband signal 10806, and controlsignal 10809 are input to frame configurator 10810, and frameconfigurator 10810 performs the rearrangement on the frequency and timeaxes based on the frame configuration information included in thecontrol signal, and outputs (quadrature) baseband signal 10811_1 (themapped signal, namely, the baseband signal based on the modulationscheme used) of stream 1 and (quadrature) baseband signal 10811_2 (themapped signal, namely, the baseband signal based on the modulationscheme used) of stream 2 according to the frame configuration.

Baseband signal 10811_1 of stream 1, baseband signal 10811_2 of stream2, and control signal 10809 are input to signal processor 10812, andsignal processor 10812 outputs post-signal-processing modulated signal 1(10813_1) and post-signal-processing modulated signal 2 (108313_2) basedon the transmission method information included in control signal 7609.

The operation of signal processor 10812 is described in detail later.

Post-signal-processing modulated signal 1 (10813_1) and control signal10809 are input to pilot inserter 10814_1, and pilot inserter 10814_1inserts the pilot symbol in post-signal-processing modulated signal 1(10813_1) based on the pilot symbol inserting method informationincluded in control signal 10809, and outputs pilot-symbol-insertedmodulated signal 10815_1.

Post-signal-processing modulated signal 2 (10813_2) and control signal10809 are input to pilot inserter 10814_2, and pilot inserter 10814_2inserts the pilot symbol in post-signal-processing modulated signal 1(10813_2) based on the pilot symbol inserting method informationincluded in control signal 10809, and outputs pilot-symbol-insertedmodulated signal 10815_2.

Pilot-symbol-inserted modulated signal 10815_1 and control signal 10809are input to IFFT (Inverse Fast Fourier Transform) section 10816_1, andIFFT (Inverse Fast Fourier Transform) section 10816_1 performs the IFFTbased on the IFFT method information included in control signal 10809,and outputs post-IFFT signal 10816_1.

Pilot-symbol-inserted modulated signal 10815_2 and control signal 10809are input to IFFT section 10816_2, and IFFT section 10816_2 performs theIFFT based on the IFFT method information included in control signal10809, and outputs post-IFFT signal 10817_2.

Post-IFFT signal 10817_1 and control signal 10809 are input to PAPRreducer 10818_1, and PAPR reducer 10818_1 performs PAPR reducingprocessing on post-IFFT signal 10817_1 based on the PAPR reductioninformation included in control signal 10809, and outputs PAPR-reducedsignal 10819_1.

Post-IFFT signal 10817_2 and control signal 10809 are input to PAPRreducer 10818_2, and PAPR reducer 10818_2 performs PAPR reducingprocessing on post-IFFT signal 10817_2 based on the PAPR reductioninformation included in control signal 10809, and outputs PAPR-reducedsignal 10819_2.

PAPR-reduced signal 10819_1 and control signal 10809 are input to guardinterval inserter 10820_1, and guard interval inserter 10820_1 insertsthe guard interval in PAPR-reduced signal 10819_1 based on the guardinterval inserting method information included in control signal 10809,and outputs guard-interval-inserted signal 10821_1.

PAPR-reduced signal 10819_2 and control signal 10809 are input to guardinterval inserter 10820_2, and guard interval inserter 10820_2 insertsthe guard interval in PAPR-reduced signal 10819_2 based on the guardinterval inserting method information included in control signal 10809,and outputs guard-interval-inserted signal 10821_2.

Guard-interval-inserted signal 10821_1, guard-interval-inserted signal10821_2, and P1 symbol transmission data 10807 are input to P1 symbolinserter 10822, and P1 symbol inserter 10822 generates the signal of theP1 symbol from P1 symbol transmission data 10807, adds the P1 symbolsignal to guard-interval-inserted signal 10821_1, adds the P1 symbol toP1-symbol-added signal 10823_1 and guard-interval-inserted signal10821_2, and outputs P1-symbol-added signal 10823_2. The signal of theP1 symbol may be added to both or one of P1-symbol-added signal 10823_1and P1-symbol-added signal 10823_2. In the case that the signal of theP1 symbol is added to one of P1-symbol-added signal 10823_1 andP1-symbol-added signal 10823_2, in an interval of the signal to whichthe P1 symbol is added, the signal of zero exists as the baseband signalin the signal to which the P1 symbol is not added.

P1-symbol-added signal 10823_1 is input to radio processor 10824_1, andradio processor 10824_1 performs the pieces of processing such as thefrequency conversion and the amplification on P1-symbol-added signal10823_1, and outputs transmitted signal 10825_1. Transmitted signal10825_1 is output as a radio wave from antenna 10826_1.

P1-symbol-added signal 10823_2 is input to radio processor 10824_2, andradio processor 10824_2 performs the pieces of processing such as thefrequency conversion and the amplification on P1-symbol-added signal10823_2, and outputs transmitted signal 10825_2. Transmitted signal10825_2 is output as a radio wave from antenna 10826_2.

For example, it is assumed that each broadcasting station transmits thesymbol with the frame configuration in FIG. 106 . FIG. 109 illustratesan example of the frame configuration on the frequency-time axis whenthe broadcasting station transmits two modulated signals described inthe first to eleventh exemplary embodiments, namely, PLP (#1 is changedto $1 in order to avoid confusion) $1 and PLP $K from two antennas.

As illustrated in FIG. 109 , a slot (symbol) exists in PLP $1, carrier 3at clock time T is a head (124501) of the slot, and carrier 4 at clocktime (T+4) is an end (124502) of the slot.

That is, a first slot is carrier 3 at clock time T for PLP $1, a secondslot is carrier 4 at clock time T, a third slot is carrier 5 at clocktime T, . . . , a seventh slot is carrier 1 at clock time (T+1), aneighth slot is carrier 2 at clock time (T+1), a ninth slot is carrier 3at clock time (T+1), . . . , a fourteenth slot is carrier 8 at clocktime (T+1), a fifteenth slot is carrier 0 at clock time (T+2), . . . .

As illustrated in FIG. 109 , a slot (symbol) exists in PLP $K, carrier 4at clock time S is a head (124503) of the slot, and carrier 4 at clocktime (S+8) is an end (124504) of the slot.

That is, a first slot is carrier 4 at clock time S for PLP $K, a secondslot is carrier 5 at clock time S, a third slot is carrier 6 at clocktime S, . . . , a fifth slot is carrier 8 at clock time S, a ninth slotis a carrier 1 at clock time (S+1), a tenth slot is carrier 2 at clocktime (S+1), . . . , a sixteenth slot is carrier 8 at clock time (S+1), aseventeenth slot is carrier 0 at clock time (S+2), . . . .

The information about the slot used in each PLP including theinformation about the leading slot (symbol) of each PLP and theinformation about the last slot (symbol) is transmitted by controlsymbols such as the P1 symbol, the P2 symbol, and the control symbolgroup.

The operation of signal processor 10812 in FIG. 108 will be describedbelow. It is assumed that signal processor 10812 includes an encoder forthe LDPC code, a mapper, a precoder, a bit length adjuster, andinterleaver.

Control signal 10809 is input to signal processor 10812, and signalprocessor 10812 decides the signal processing method based on the codelength (block length) of the LDPC code, the transmission methodinformation (SISO transmission, MIMO transmission, and MISOtransmission), the modulation scheme information, and the like, whichare included in control signal 10809. In the case that the MIMOtransmission is selected as the transmission scheme, based on the codelength (block length) of the LDPC code, the modulation scheme set, andone of the bit length adjusting methods of the first to eleventhexemplary embodiments, signal processor 10812 adjusts the bit length,performs the interleaving and the mapping, performs the precoding forsome situations, and outputs post-signal-processing modulated signal 1(10813_1) and post-signal-processing modulated signal 2 (10813_2).

As described above, the method for transmitting each PLP (for example,the transmission method for transmitting one stream, the transmissionmethod in which the time-space block code is used, and the method fortransmitting two streams) and the information about the currently-usedmodulation scheme are transmitted to the terminal using the P1 symbol,the P2 symbol, and the control symbol group.

The operation of the terminal at that time will be described below.

Referring to FIG. 110 , post-signal-processing signals 11004_X and11004_Y that are of the signals transmitted from broadcasting station(FIG. 108 ) are input to P1 symbol detector and decoder 11011, and P1symbol detector and decoder 11011 detects the P1 symbol to perform thesignal detection and time-frequency synchronization, obtains the controlinformation included in the P1 symbol (by performing the demodulationand the error correction decoding), and outputs P1 symbol controlinformation 11012.

Received signal 11002_X received with antenna 11001_X is input toOFDM-scheme-associated processor 11003_X, and OFDM-scheme-associatedprocessor 11003_X performs the reception-side signal processing for theOFDM scheme, and outputs post-signal-processing signal 11004_X.Similarly, received signal 11002_Y received with antenna 11001_Y isinput to OFDM-scheme-associated processor 11003_Y, andOFDM-scheme-associated processor 11003_Y performs the reception-sidesignal processing for the OFDM scheme, and outputspost-signal-processing signal 11004_Y.

P1 symbol control information 11012 is input to OFDM-scheme-associatedprocessors 11003_X and 11003_Y, and OFDM-scheme-associated processors11003_X and 11003_Y change the signal processing method for the OFDMscheme based on P1 symbol control information 11012 (as described above,this is because the P1 symbol includes the information about the methodfor transmitting the signal transmitted from the broadcasting station).

Post-signal-processing signals 11004_X and 11004_Y and P1 symbol controlinformation 11012 are input to P2 symbol demodulator 11013, and P2symbol demodulator 11013 performs the signal processing based on the P1symbol control information, performs the demodulation (including theerror correction decoding), and outputs P2 symbol control information11014.

P1 symbol control information 11012 and P2 symbol control information11014 are input to control information generator 11015, and controlinformation generator 11015 bundles the pieces of control information(about the reception operation), and outputs the bundled controlinformation as control signal 11016. As illustrated in FIG. 110 ,control signal 11016 is input to each section.

Post-signal-processing signal 11004_X and control signal 11016 are inputto channel variation estimator 11005_1 for modulated signal z₁(modulated signal z₁ is described in exemplary embodiment A1), andchannel variation estimator 11005_1 for modulated signal z₁ estimatesthe channel variation between the antenna from which the transmittertransmits modulated signal z₁ and receiving antenna 11001_X using thepilot symbol included in post-signal-processing signal 11004_X, andoutputs channel estimation signal 11006_1.

Post-signal-processing signal 11004_X and control signal 11016 are inputto channel variation estimator 11005_2 for modulated signal z₂(modulated signal z₂ is described in exemplary embodiment A1), andchannel variation estimator 11005_2 for modulated signal z₂ estimatesthe channel variation between the antenna from which the transmittertransmits modulated signal z₂ and receiving antenna 11001_X using thepilot symbol included in post-signal-processing signal 11004_X, andoutputs channel estimation signal 11006_2.

Post-signal-processing signal 11004_Y and control signal 11016 are inputto channel variation estimator 11007_1 for modulated signal z₁(modulated signal z₁ is described in exemplary embodiment A1), andchannel variation estimator 11007_1 for modulated signal z₁ estimatesthe channel variation between the antenna from which the transmittertransmits modulated signal z₁ and receiving antenna 11001_Y using thepilot symbol included in post-signal-processing signal 11004_Y, andoutputs channel estimation signal 11008_1.

Post-signal-processing signal 11004_Y and control signal 11016 are inputto channel variation estimator 11007_2 for modulated signal z₂(modulated signal z₂ is described in exemplary embodiment A1), andchannel variation estimator 11007_2 for modulated signal z₂ estimatesthe channel variation between the antenna from which the transmittertransmits modulated signal z₂ and receiving antenna 11001_Y using thepilot symbol included in post-signal-processing signal 11004_Y, andoutputs channel estimation signal 11008_2.

Signals 11006_1, 11006_2, 11008_1, 11008_2, 11004_X, and 11004_Y andcontrol signal 11016 are input to signal processor 11009, and signalprocessor 11009 performs the demodulation and the decoding based on thepieces of information, such as the transmission scheme, the modulationscheme, the error correction coding scheme, the error correction codingrate, and the block size of the error correction code, which areincluded in control signal 11016 and used to transmit each PLP, andoutputs received data 11010. The receiver extracts the necessary PLPfrom the information about the slot, which is included in the controlsymbols such as the P1 symbol, the P2 symbol, and the control symbolgroup and used by each PLP, demodulates (including signal separation andsignal detection) the PLP, and performs the error correction decoding.

The configuration of the transmitter to which the transmission method inwhich the precoding and the phase change are performed is applied (forexample, in the broadcasting station pursuant to the DVB-T2 standard)and the configuration of the receiver that receives the signaltransmitted from the transmitter are mainly described above.

In the case that the broadcasting system in which the DVB-T2 standard isused is operated while the receiver that can receive the modulatedsignal pursuant to the DVB-T2 standard becomes already widespread, it isdesirable that the receiver that can receive the modulated signalpursuant to the DVB-T2 standard is not influenced when a new standard isintroduced.

A method for configuring the P1 symbol (P1 signalling data) and the P2symbol (L1 pre-signalling data and L1 post-signalling data) in which thetransmission method for transmitting one stream and the transmissionmethod for transmitting two streams are introduced without influencingthe receiver that can receive the modulated signal pursuant to theDVB-T2 standard and a method for configuring the P1 symbol (P1signalling data) and the P2 symbol (L1 pre-signalling data and L1post-signalling data) in which the bit length adjusting methods of thefirst to eleventh exemplary embodiments will be described below.

In the DVB-T2 standard, an S1 field of the P1 symbol (P1 signallingdata) is specified as follows.

TABLE 1 VALUE OF S1 TYPE DESCRIPTION 000 T2_SISO The transmitter sets S1to the value (“000”) such that the receiver recognizes that themodulated signal is transmitted using the SISO transmission scheme inthe DVB-T2 standard. 001 T2_MISO The transmitter sets S1 to the value(“001”) such that the receiver recognizes that the modulated signal istransmitted using the MISO transmission scheme in the DVB-T2 standard.010 Reserved Usable in a future system 011 100 101 110 111

In TABLE 1, the SISO scheme is one in which one stream is transmittedusing one antenna or a plurality of antennas, and the MISO scheme is onein which a plurality of modulated signals are generated using thespace-time (or space-frequency) block code of NPLs 5, 7, and 8 totransmit the modulated signals using a plurality of antennas.

A type of the FEC (Forward Error Correction) used in the PLP isspecified by two bits of PLP_FEC_TYPE of the P2 symbol L1post-signalling data.

TABLE 2 VALUE OF PLP_FEC_TYPE PLP FEC TYPE 00 The transmitter sets thevalue of PLP_FEC_TYPE to the value (“00”) in order that the receiverrecognizes the use of the LDPC code having the block length of 16k(16200 bits). 01 The transmitter sets the value of PLP_FEC_TYPE to thevalue (“01”) in order that the receiver recognizes the use of the LDPCcode having the block length of 64k (64800 bits). 10 Reserved 11

The configurations of the P1 symbol and P2 symbol for the purpose of thebit length adjustment described in the first to eleventh exemplaryembodiments without influencing the receiver that can receive themodulated signal pursuant to the DVB-T2 standard will be describedbelow.

The S1 field of the P1 symbol (P1 signalling data) in the DVB-T2standard is described above. In the DVB standard, the S1 field of the P1symbol (P1 signalling data) is further specified as follows.

TABLE 3-1 VALUE OF S1 TYPE DESCRIPTION 000 T2_SISO The transmitter setsS1 to the value (“000”) such that the receiver recognizes that themodulated signal is transmitted using the SISO transmission scheme inthe DVB-T2 standard. 001 T2_MISO The transmitter sets S1 to the value(“001”) such that the receiver recognizes that the modulated signal istransmitted using the MISO transmission scheme in the DVB-T2 standard.010 Non-T2 SPECIAL MODE 011 T2_LITE_SISO The transmitter sets S1 to thevalue (“011”) such that the receiver recognizes that the modulatedsignal is transmitted using the SISO transmission scheme in the DVB-T2Lite standard.

TABLE 3-2 VALUE OF S1 TYPE DESCRIPTION 100 T2_LITE_MISO The transmittersets S1 to the value (“100”) such that the receiver recognizes that themodulated signal is transmitted using the MISO transmission scheme inthe DVB-T2 Lite standard. 101 NGH_SISO The transmitter sets S1 to thevalue (“101”) such that the receiver recognizes that the modulatedsignal is transmitted using the SISO transmission scheme in the DVB-NGHstandard. 110 NGH_MISO The transmitter sets S1 to the value (“110”) suchthat the receiver recognizes that the modulated signal is transmittedusing the MISO transmission scheme in the DVB-NGH standard. 111 ESC Thetransmitter sets S1 to the value (“111”) in the case that a transmissionscheme except for the transmission schemes defined in 000-110 isselected in S1.

In TABLES 3-1 and 3-2, the SISO scheme is one in which one stream istransmitted using one antenna or a plurality of antennas, and the MISOscheme is one in which a plurality of modulated signals are generatedusing the space-time (or space-frequency) block code of NPLs 5, 7, and 8to transmit the modulated signals using a plurality of antennas.

In the case that s2 field 1 and s2 field 2 are set for a new standardwhile S1 is set to the value (“111”) in TABLES 3-1 and 3-2, thedefinition is as follows.

TABLE 4-1 S2 field 1 S2 field 2 MEANING DESCRIPTION 000 x Preambleformat When S1 has the value “111” of the NGH while S2 field 1 and S2field 2 MIMO signal have the values “000” and “x”, the receiverrecognizes that the modulated signal is transmitted using the MIMOtransmission scheme in the DVB-NGH standard. When transmitting themodulated signal using the MIMO transmission scheme in the DVB-NGHstandard, the transmitter sets S1, S2 field 1, and S2 field 2 to thevalues “111”, “000”, and “x”, respectively. 001 x Preamble format WhenS1 has the value “111” of the NGH while S2 field 1 and S2 field 2 hybridSISO have the values “001” and “x”, signal the receiver recognizes thatthe modulated signal is transmitted using the hybrid SISO transmissionscheme in the DVB-NGH standard. When transmitting the modulated signalusing the hybrid SISO transmission scheme in the DVB-NGH standard, thetransmitter sets S1, S2 field 1, and S2 field 2 to the values “111”,“001”, and “x”, respectively.

TABLE 4-2 S2 field 1 S2 field 2 MEANING DESCRIPTION 010 x Preambleformat When S1 has the value “111” of the NGH while S2 field 1 and S2field hybrid MISO 2 have the values “010” and signal “x”, the receiverrecognizes that the modulated signal is transmitted using the hybridMISO transmission scheme in the DVB-NGH standard. When transmitting themodulated signal using the hybrid MISO transmission scheme in theDVB-NGH standard, the transmitter sets S1, S2 field 1, and S2 field 2 tothe values “111”, “010”, and “x”, respectively. 011 x Preamble formatWhen S1 has the value “111” of the NGH while S2 field 1 and S2 field 2hybrid MIMO have the values “011” and “x”, signal the receiverrecognizes that the modulated signal is transmitted using the hybridMIMO transmission scheme in the DVB-NGH standard. When transmitting themodulated signal using the hybrid MIMO transmission scheme in theDVB-NGH standard, the transmitter sets S1, S2 field 1, and S2 field 2 tothe values “111”, “011”, and “x”, respectively.

TABLE 4-3 S2 field 1 S2 field 2 MEANING DESCRIPTION 100 x Ω STANDARDWhen S1 has the value “111” SISO while S2 field 1 and S2 field 2 havethe values “100” and “x”, the receiver recognizes that the modulatedsignal is transmitted using the SISO transmission scheme in the Ωstandard. When transmitting the modulated signal using the SISOtransmission scheme in the Ω standard, the transmitter sets S1, S2 field1, and S2 field 2 to the values “111”, “100”, and “x”, respectively. 101x Ω STANDARD When S1 has the value “111” MISO while S2 field 1 and S2field 2 have the values “101” and “x”, the receiver recognizes that themodulated signal is transmitted using the MISO transmission scheme inthe Ω standard. When transmitting the modulated signal using the MISOtransmission scheme in the Ω standard, the transmitter sets S1, S2 field1, and S2 field 2 to the values “111”, “101”, and “x”, respectively.

TABLE 4-4 S2 field 1 S2 field 2 MEANING DESCRIPTION 110 x Ω STANDARDWhen S1 has the value MIMO “111” while S2 field 1 and S2 field 2 havethe values “110” and “x”, the receiver recognizes that the modulatedsignal is transmitted using the MIMO transmission scheme in the Ωstandard. When transmitting the modulated signal using the MIMOtransmission scheme in the Ω standard, the transmitter sets S1, S2 field1, and S2 field 2 to the values “111”, “110”, and “x”, respectively. 111x Reserved For future extension

In TABLES 4-1 to 4-4, “x” means an unsettled value (any value), the SISOscheme is one in which one stream is transmitted using one antenna or aplurality of antennas, the MISO scheme is one in which a plurality ofmodulated signals are generated using the space-time (orspace-frequency) block code of NPLs 5, 7, and 8 to transmit themodulated signals using a plurality of antennas, and the MIMO scheme isone in which the two streams subjected to, for example, the actualprecoding are transmitted.

Thus, using the P1 symbol transmitted from the transmitter, the receivercan recognize which one of the transmission method for transmitting theone stream and the transmission method for transmitting two streams isused to transmit the modulated signal.

As described above, when the transmission method for transmitting onestream, the SISO scheme (the scheme in which the one stream istransmitted using one antenna or a plurality of antennas), the MISOscheme (the scheme in which a plurality of modulated signals aregenerated using the space-time (or space-frequency) block code of NPLsX1 and X2 to transmit the modulated signals using a plurality ofantennas), or the MIMO transmission scheme is selected, the two bits ofPLP_FEC_TYPE of the P2 symbol L1 post-signalling data are defined asfollows (the method for setting S1 and s2 of the P1 symbol is describedin TABLES 3-1, 3-2, and 4-1 to 4-4).

TABLE 5 VALUE OF PLP_FEC_TYPE PLP FEC TYPE 00 The transmitter sets thevalue of PLP_FEC_TYPE to the value (“00”) in order that the receiverrecognizes the use of the LDPC code having the block length of 16k(16200 bits). 01 The transmitter sets the value of PLP_FEC_TYPE to thevalue (“01”) in order that the receiver recognizes the use of the LDPCcode having the block length of 64k (64800 bits). 10 Reserved 11Reserved

The three bits of PLP_NUM_PER_CHANNEL_USE of the P2 symbol L1post-signalling data is defined as follows.

TABLE 6-1 BPCU VALUE OF (Bit Per Channel Use) PLP_NUM_PER_CHANNEL_USE(VALUE OF X + Y) Modulation 000 6 When PLP_NUM_PRE_CHANNEL_USE has thevalue (“000”), the Tx1 modulation scheme is set to QPSK, and the Tx2modulation scheme is set to 16QAM. (When PLP_NUM_PRE_CHANNEL_USE has thevalue (“000”), the s1 modulation scheme is set to QPSK, and the s2modulation scheme is set to 16QAM.) 001 8 When PLP_NUM_PRE_CHANNEL_USEhas the value (“000”), the Tx1 modulation scheme is set to 16QAM, andthe Tx2 modulation scheme is set to 16QAM. (When PLP_NUM_PRE_CHANNEL_USEhas the value (“000”), the s1 modulation scheme is set to 16QAM, and thes2 modulation scheme is set to 16QAM.)

TABLE 6-2 BPCU VALUE OF (Bit Per Channel Use) PLP_NUM_PRE_CHANNEL_USE(VALUE OF X + Y) Modulation 010 10 When PLP_NUM_PRE_CHANNEL_USE has thevalue (“000”), the Tx1 modulation scheme is set to 16QAM, and the Tx2modulation scheme is set to 64QAM. (When PLP_NUM_PRE_CHANNEL_USE has thevalue (“000”), the s1 modulation scheme is set to 16QAM, and the s2modulation scheme is set to 64QAM.) 011 12 When PLP_NUM_PRE_CHANNEL_USEhas the value (“000”), the Tx1 modulation scheme is set to 64QAM, andthe Tx2 modulation scheme is set to 64QAM. (When PLP_NUM_PRE_CHANNEL_USEhas the value (“000”), the s1 modulation scheme is set to 64QAM, and thes2 modulation scheme is set to 64QAM.)

TABLE 6-3 BPCU (Bit Per VALUE OF Channel Use) PLP_NUM_PRE_CHANNEL_USE(VALUE OF X + Y) Modulation 100 14 When PLP_NUM_PRE_CHANNEL_USE has thevalue (“000”), the Tx1 modulation scheme is set to 64QAM, and the Tx2modulation scheme is set to 256QAM. (When PLP_NUM_PRE_CHANNEL_USE hasvalue (“000”), the s1 modulation scheme is set to 64QAM, and the s2modulation scheme is set to 256QAM.) 101 16 When PLP_NUM_PRE_CHANNEL_USEhas the value (“000”), the Tx1 modulation scheme is set to 256QAM, andthe Tx2 modulation scheme is set to 256QAM. (WhenPLP_NUM_PRE_CHANNEL_USE has the value (“000”), the s1 modulation schemeis set to 256QAM, and the s2 modulation scheme is set to 256QAM.)101-111 Reserved Reserved

It is assumed that the value of (X+Y), s1, and s2 are similar to thoseof the first to third exemplary embodiments.

Accordingly, in the case that Ω standard MIMO transmission scheme isassigned by the P1 symbol, signal processor 10812 in FIG. 108 adjuststhe bit length (the number of bits of the adjustment bit string) by oneof the bit length adjusting methods of the first to eleventh exemplaryembodiments using the block length of the LDPC code assigned by the twobits of PLP_FEC_TYPE of the P2 symbol L1 post-signalling data and the s1and s2 modulation schemes assigned by the three bits ofPLP_NUM_PER_CHANNEL_USE of the P2 symbol L1 post-signalling data,performs the interleaving and the mapping, performs the precoding forsome situations, and outputs post-signal-processing modulated signal 1(10813_1) and post-signal-processing modulated signal 2 (10813_2).

The specific numerical examples of the bit length adjustment (theadjustment of the number of bits of the adjustment bit string) aredescribed in the first to eleventh exemplary embodiments. However, thespecific numerical examples are described only by way of example.

In the terminal receiver of FIG. 110 , P1 symbol detector and decoder11011 and P2 symbol demodulator 11013 obtain the P1 symbol, PLP_FEC_TYPEof the P2 symbol L1 post-signalling data, and PLP_NUM_PER_CHANNEL_USE ofthe P2 symbol L1 post-signalling data, control signal generator 11015estimates the bit length adjusting method used in the transmitter basedon the pieces of data, and signal processor 11009 performs the signalprocessing based on the estimated bit length adjusting method. Thedetailed signal processing is described in the operation examples of thereceivers of the first to eleventh exemplary embodiments.

Therefore, the transmitter can efficiently transmit the modulated signalof the new standard in addition to the modulated signal based on theDVB-T2 standard, namely, the pieces of control information of the P1 andP2 symbols can be reduced. The effects of the first to eleventhexemplary embodiments can also be obtained in transmitting the modulatedsignal of the new standard.

Additionally, the receiver can determine whether the received signal isthe signal of the DVB-T2 standard or the signal of the new standardusing the P1 and P2 symbols, and the effects of the first to eleventhexemplary embodiments can be obtained.

The bit length adjustments of the first to eleventh exemplaryembodiments are performed, and the broadcasting station transmits themodulated signal. Therefore, in the terminal receiver, theconfigurations of the P1 symbol control information and P2 symbolcontrol information can be reduced because of the clear symbolconstituting each block of the block code such as the LDPC code (absenceof the symbol constructed with the pieces of data of the plurality ofblocks) (for presence of the symbol constructed with the pieces of dataof the plurality of blocks, it is necessary to add information about theframe configuration at that time).

The configurations of the P1 and P2 symbols of the twelfth exemplaryembodiment are described only by way of example. Alternatively, the P1and P2 symbols of the twelfth exemplary embodiment may be configured byanother method. A symbol used to transmit the control information maynewly be added to the transmission frame while the control informationis transmitted using the P1 and P2 symbols.

(Supplement 1)

The plurality of exemplary embodiments may be combined.

In the description, “∀” designates a universal quantifier, and “∃”designates an existential quantifier.

In the description, for example, “radian” is used in a phase unit suchas an argument on a complex plane.

The use of the complex plane can display a polar coordinate of thecomplex number in terms of a polar form. Assuming that point (a, b) onthe complex plane is represented as [r,θ] in terms of the polarcoordinate when complex number z=a+jb (a and b are a real number and jis an imaginary unit) corresponds to point (a, b), the followingequation holds:a=r×cos θb=r×sin θr=√{square root over (a ² +b ²)}  [Mathematical Formula 364]

where r is an absolute value of z (r=|z|) and θ is an argument, andz=a+jb is represented as (r×e^(jθ)).

In the present disclosure, baseband signals s1, s2, z1, and z2 are acomplex signal, and the complex signal is represented as I+jQ (j is animaginary unit) when I is the in-phase signal while Q is the quadraturesignal. At this point, I may be zero, and Q may be zero.

For example, a program executing the above communication method ispreviously stored in a ROM (Read Only Memory), and the program may beoperated with a CPU (Central Processing Unit).

The program executing the above communication method is stored in acomputer-readable storage medium, the program stored in the storagemedium is recorded in a RAM (Random Access Memory) of a computer, andthe computer may be operated according to the program.

Typically, each of the configurations of the above exemplary embodimentsmay be implemented as LSI (Large Scale Integration) that is of anintegrated circuit. The configuration of each exemplary embodiment mayseparately be formed into one chip, or a whole or part of theconfiguration of each exemplary embodiment may separately be formed intoone chip.

Although the term of LSI is used, sometimes the terms of IC (IntegratedCircuit), system LSI, super LSI, and ultra LSI are used depending on adegree of integration. A technique of integrating the circuit is notlimited to LSI, but the technique may be performed by a dedicatedcircuit or a general-purpose processor. A programmable FPGA (FieldProgrammable Gate Array) or a reconfigurable processor that canreconfigure connection and setting of circuit cell in LSI may be usedafter the production of LSI.

When a circuit integrating technology with which LSI is replaced is putinto use by the progress of the semiconductor technology or a derivativetechnology, the functional block may be integrated using the technology.Possibly a biotechnology may be applied.

The bit length adjusting method is described in the first to eleventhexemplary embodiments. The method for applying the bit length adjustingmethods of the first to eleventh exemplary embodiments to the DVBstandard is described in the twelfth exemplary embodiment. The case that16QAM, 64QAM, and 256QAM are applied as the modulation scheme isdescribed in the above exemplary embodiments.

In the first to twelfth exemplary embodiments, the modulation schemehaving the 16 signal points may be used instead of 16QAM in the I-Qplane. Similarly, n the first to twelfth exemplary embodiments, themodulation scheme having the 64 signal points may be used instead of64QAM in the I-Q plane, and the modulation scheme having the 256 signalpoints may be used instead of 256QAM in the I-Q plane.

Alternatively, one antenna may be constructed with a plurality ofantennas.

Alternatively, the receiver and the antenna may separately beconfigured. For example, the receiver includes an interface that inputsthe signal received with the antenna and the signal in which thefrequency conversion performed on the signal received with the antennathrough a cable, and the receiver performs the subsequent processing.

The data and information, which are obtained with the receiver, areconverted into video and audio, and displayed on a display (monitor) oroutput as sound from a speaker. The data and information, which areobtained with the receiver, may be subjected to the signal processingassociated with the video or audio (the signal processing does not needto be performed), and output from an RCA terminal (video terminal andaudio terminal), USB (Universal Serial Bus), HDMI (registered trademark)(High-Definition Multimedia Interface), and digital terminal, which areincluded in the receiver.

(Supplement 2)

The bit length adjusting method is described in the first to eleventhexemplary embodiments. The method for applying the bit length adjustingmethods of the first to eleventh exemplary embodiments to the DVBstandard is described in the twelfth exemplary embodiment. The case that16QAM, 64QAM, and 256QAM are applied as the modulation scheme isdescribed in the above exemplary embodiments. A specific mapping methodwith respect to 16QAM, 64QAM, and 256QAM is described in (Configurationexample R1).

A specific mapping method with respect to 16QAM, 64QAM, and 256QAMdifferent from that of (Configuration example R1) will be describedbelow. The following 16QAM, 64QAM, and 256QAM may be applied to thefirst to twelfth exemplary embodiments, and the effects of the first totwelfth exemplary embodiments can also be obtained.

The case that 16QAM is extended will be described.

The 16QAM mapping method will be described below. FIG. 111 illustratesan arrangement example of 16QAM signal points in the I-Q plane. In FIG.111 , 16 marks “◯” indicate 16QAM signal points, a horizontal axisindicates I, and a vertical axis indicates Q. In FIG. 111 , it isassumed that f>0 (f is a real number larger than 0), f≠3, and f≠1 hold.

In the I-Q plane, 16 signal points included in 16QAM (indicated by themarks “◯” in FIG. 111 ) are obtained as follows. (w_(16a) is a realnumber larger than 0)

(3×w_(16a),3×w_(16a)), (3×w_(16a),f×w_(16a)), (3×w_(16a),−f×w_(16a)),(3×w_(16a),−3×w_(16a)), (f×w_(16a),3×w_(16a)), (f×w_(16a),f×w_(16a)),(f×w_(16a),−f×w_(16a)), (f×w_(16a),−3×w_(16a)), (−f×w_(16a),3×w_(16a)),(−f×w_(16a),f×w_(16a)), (−f×w_(16a),−f×w_(16a)),(−f×w_(16a),−3×w_(16a)), (−3×w_(16a),3×w_(16a)), (−3×w_(16a),f×w_(16a)),(−3×w_(16a),−f×w_(16a)), (−3×w_(16a),−3×w_(16a))

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, and b3. For example, for the bits to be transmitted (b0, b1, b2,b3)=(0,0,0,0), the bits are mapped at signal point 11101 in FIG. 111 ,and (I,Q)=(3×w_(16a), 3×w_(16a)) is obtained when I is an in-phasecomponent while Q is a quadrature component of the mapped basebandsignal.

Based on the bits to be transmitted (b0, b1, b2, b3), in-phase componentI and quadrature component Q of the mapped baseband signal are decided(during 16QAM modulation). FIG. 111 illustrates an example of therelationship between the set of b0, b1, b2, and b3 (0000 to 1111) andthe signal point coordinates. Values 0000 to 1111 of the set of b0, b1,b2, and b3 are indicated immediately below 16 signal points included in16QAM (the marks “◯” in FIG. 111 ) (3×w_(16a),3×w_(16a)),(3×w_(16a),f×w_(16a)), (3×w_(16a),−f×w_(16a)), (3×w_(16a),−3×w_(16a)),(f×w_(16a),3×w_(16a)), (f×w_(16a),f×w_(16a)), (f×w_(16a), −f×w_(16a)),(f×w_(16a), −3×w_(16a)), (−f×w_(16a),3×w_(16a)), (−f×w_(16a),f×w_(16a)),(−f×w_(16a),−f×w_(16a)), (−f×w_(16a), −3×w_(16a)),(−3×w_(16a),3×w_(16a)), (−3×w_(16a),f×w_(16a)), (−3×w_(16a),−f×w_(16a)),(−3×w_(16a),−3×w_(16a)). Respective coordinates of the signal points(“◯”) immediately above the values 0000 to 1111 of the set of b0, b1,b2, and b3 in the I-Q plane serve as in-phase component I and quadraturecomponent Q of the mapped baseband signal. The relationship between theset of b0, b1, b2, and b3 (0000 to 1111) and the signal pointcoordinates during 16QAM modulation is not limited to that in FIG. 111 .

16 signal points in FIG. 111 are named as “signal point 1”, “signalpoint 2”, . . . , “signal point 15”, and “signal point 16” (because ofthe presence of 16 signal points, “signal point 1” to “signal point 16”exist). In the I-Q plane, Di is a distance between “signal point i” andthe origin. At this point, w_(16a) is given by the following equation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 365} \right\rbrack & \; \\\begin{matrix}{w_{16\; a} = \frac{z}{\sqrt{\frac{\sum\limits_{i = 1}^{16}D_{i}^{2}}{16}}}} \\{= \frac{z}{\sqrt{\frac{\left( {{\left( {3^{2} + 3^{2}} \right) \times 4} + {\left( {f^{2} + f^{2}} \right) \times 4} + {\left( {f^{2} + 3^{2}} \right) \times 8}} \right)}{16}}}}\end{matrix} & ({H1})\end{matrix}$

Therefore, the mapped baseband signal has an average power of z₂.

In the above description, the case equal to (Configuration example R1)is referred to as uniform-16QAM, and other cases are referred to asnon-uniform 16QAM.

The 64QAM mapping method will be described below. FIG. 112 illustratesan arrangement example of 64QAM signal points in the I-Q plane. In FIG.112 , 64 marks “◯” indicate 64QAM signal points, a horizontal axisindicates I, and a vertical axis indicates Q. In FIG. 112 , it isassumed that g₁>0 (g₁ is a real number larger than 0), g₂>0 (g₂ is areal number larger than 0), and g₃>0 (g₃ is a real number larger than 0)hold, and that {{g₁≠7 and g₂≠7 and g₃≠7} holds}

and {{(g₁,g₂,g₃)≠(1,3,5) and (g₁,g₂,g₃)≠(1,5,3) and (g₁,g₂,g₃)≠(3,1,5)and (g₁,g₂,g₃)≠(3,5,1) and (g₁,g₂,g₃)≠(5,1,3) and (g₁,g₂,g₃)≠(5,3,1)}hold}

and {{g₁≠g₂ and g₁≠g₃ and g₂≠g₃} holds}.

In the I-Q plane, 64 signal points included in 64QAM (indicated by themarks “◯” in FIG. 112 ) are obtained as follows. (w_(64a) is a realnumber larger than 0)

(7×w_(64a),7×w_(64a)), (7×w_(64a),g₃×w_(64a)), (7×w_(64a),g₂×w_(64a)),(7×w_(64a),g₁×w_(64a)), (7×w_(64a),−g₁×w_(64a)),(7×w_(64a),−g₂×w_(64a)), (7×w_(64a),−g₃×w_(64a)), (7×w_(64a),−7×w_(64a))

(g₃×w_(64a),7×w_(64a)), (g₃×w_(64a),g₃×w_(64a)),(g₃×w_(64a),g₂×w_(64a)), (g₃×w_(64a),g₁×w_(64a)),(g₃×w_(64a),−g₁×w_(64a)), (g₃×w_(64a),−g₂×w_(64a)),(g₃×w_(64a),−g₃×w_(64a)), (g₃×w_(64a),−7×w_(64a))

(g₂×w_(64a),7×w_(64a)), (g₂×w_(64a),g₃×w_(64a)),(g₂×w_(64a),g₂×w_(64a)), (g₂×w_(64a),g₁×w_(64a)),(g₂×w_(64a),−g₁×w_(64a)), (g₂×w_(64a),−g₂×w_(64a)),(g₂×w_(64a),−g₃×w_(64a)), (g₂×w_(64a),−7×w_(64a))

(g₁×w_(64a),7×w_(64a)), (g₁×w_(64a),g₃×w_(64a)),(g₁×w_(64a),g₂×w_(64a)), (g₁×w_(64a),g₁×w_(64a)),(g₁×w_(64a),−g₁×w_(64a)), (g₁×w_(64a),−g₂×w_(64a)),(g₁×w_(64a),−g₃×w_(64a)), (g₁×w_(64a),−7×w_(64a))

(−g₁×w_(64a),7×w_(64a)), (−g₁×w_(64a),g₃×w_(64a)),(−g₁×w_(64a),g₂×w_(64a)), (−g₁×w_(64a),g₁×w_(64a)),(−g₁×w_(64a),−g₁×w_(64a)), (−g₁×w_(64a),−g₂×w_(64a)),(−g₁×w_(64a),−g₃×w_(64a)), (−g₁×w_(64a),−7×w_(64a))

(−g₂×w_(64a),7×w_(64a)), (−g₂×w_(64a),g₃×w_(64a)),(−g₂×w_(64a),g₂×w_(64a)), (−g₂×w_(64a),g₁×w_(64a)),(−g₂×w_(64a),−g₁×w_(64a)), (−g₂×w_(64a),−g₂×w_(64a)),(−g₂×w_(64a),−g₃×w_(64a)), (−g₂×w_(64a),−7×w_(64a))

(−g₃×w_(64a),7×w_(64a)), (−g₃×w_(64a),g₃×w_(64a)),(−g₃×w_(64a),g₂×w_(64a)), (−g₃×w_(64a),g₁×w_(64a)),(−g₃×w_(64a),−g₁×w_(64a)), (−g₃×w_(64a),−g₂×w_(64a)),(−g₃×w_(64a),−g₃×w_(64a)), (−g₃×w_(64a),−7×w_(64a))

(−7×w_(64a),7×w_(64a)), (−7×w_(64a),g₃×w_(64a)),(−7×w_(64a),g₂×w_(64a)), (−7×w_(64a),g₁×w_(64a)),(−7×w_(64a),−g₁×w_(64a)), (−7×w_(64a),−g₂×w_(64a)),(−7×w_(64a),−g₃×w_(64a)), (−7×w_(64a),−7×w_(64a))

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, for the bits to be transmitted (b0,b1, b2, b3, b4, b5)=(0,0,0,0,0,0), the bits are mapped at signal point11201 in FIG. 112 , and (I,Q)=(7×w_(64a),7×w_(64a)) is obtained when Iis an in-phase component while Q is a quadrature component of the mappedbaseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 112 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to 111111 of theset of b0, b1, b2, b3, b4, and b5 are indicated immediately below 64signal points included in 64QAM (the marks “◯” in FIG. 112 )(7×w_(64a),7×w_(64a)), (7×w_(64a),g₃×w_(64a)), (7×w_(64a),g₂×w_(64a)),(7×w_(64a),g₁×w_(64a)), (7×w_(64a),−g₁×w_(64a)),(7×w_(64a),−g₂×w_(64a)), (7×w_(64a),−g₃×w_(64a)), (7×w_(64a),−7×w_(64a))

(g₃×w_(64a),7×w_(64a)), (g₃×w_(64a),g₃×w_(64a)),(g₃×w_(64a),g₂×w_(64a)), (g₃×w_(64a),g₁×w_(64a)),(g₃×w_(64a),−g₁×w_(64a)), (g₃×w_(64a),−g₂×w_(64a)),(g₃×w_(64a),−g₃×w_(64a)), (g₃×w_(64a),−7×w_(64a))

(g₂×w_(64a),7×w_(64a)), (g₂×w_(64a),g₃×w_(64a)),(g₂×w_(64a),g₂×w_(64a)), (g₂×w_(64a),g₁×w_(64a)),(g₂×w_(64a),−g₁×w_(64a)), (g₂×w_(64a),−g₂×w_(64a)),(g₂×w_(64a),−g₃×w_(64a)), (g₂×w_(64a),−7×w_(64a))

(g₁×w_(64a),7×w_(64a)), (g₁×w_(64a),g₃×w_(64a)),(g₁×w_(64a),g₂×w_(64a)), (g₁×w_(64a),g₁×w_(64a)),(g₁×w_(64a),−g₁×w_(64a)), (g₁×w_(64a),−g₂×w_(64a)),(g₁×w_(64a),−g₃×w_(64a)), (g₁×w_(64a),−7×w_(64a))

(−g₁×w_(64a),7×w_(64a)), (−g₁×w_(64a),g₃×w_(64a)),(−g₁×w_(64a),g₂×w_(64a)), (−g₁×w_(64a),g₁×w_(64a)),(−g₁×w_(64a),−g₁×w_(64a)), (−g₁×w_(64a),−g₂×w_(64a)),(−g₁×w_(64a),−g₃×w_(64a)), (−g₁×w_(64a),−7×w_(64a))

(−g₂×w_(64a),7×w_(64a)), (−g₂λw_(64a),g₃×w_(64a)),(−g₂×w_(64a),g₂×w_(64a)), (−g₂×w_(64a),g₁×w_(64a)),(−g₂×w_(64a),−g₁×w_(64a)), (−g₂×w_(64a),−g₂×w_(64a)),(−g₂×w_(64a),−g₃×w_(64a)), (−g₂×w_(64a),−7×w_(64a))

(−g₃×w_(64a),7×w_(64a)), (−g₃×w_(64a),g₃×w_(64a)),(−g₃×w_(64a),g₂×w_(64a)), (−g₃×w_(64a),g₁×w_(64a)),(−g₃×w_(64a),−g₁×w_(64a)), (−g₃×w_(64a),−g₂×w_(64a)),(−g₃×w_(64a),−g₃×w_(64a)), (−g₃×w_(64a),−7×w_(64a))

(−7×w_(64a),7×w_(64a)), (−7×w_(64a),g₃×w_(64a)),(−7×w_(64a),g₂×w_(64a)), (−7×w_(64a),g₁×w_(64a)),(−7×w_(64a),g₁×w_(64a)), (−7×w_(64a),−g₂×w_(64a)),(−7×w_(64a),−g₃×w_(64a)), (−7×w_(64a),−7×w_(64a)). Respectivecoordinates of the signal points (“◯”) immediately above the values000000 to of the set of b0, b1, b2, b3, b4, and b5 in the I-Q planeserve as in-phase component I and quadrature component Q of the mappedbaseband signal. The relationship between the set of b0, b1, b2, b3, b4,and b5 (000000 to 111111) and the signal point coordinates during 64QAMmodulation is not limited to that in FIG. 112 .

64 signal points in FIG. 112 are named as “signal point 1”, “signalpoint 2”, . . . , “signal point 63”, and “signal point 64” (because ofthe presence of 64 signal points, “signal point 1” to “signal point 64”exist). In the I-Q plane, Di is a distance between “signal point i” andthe origin. At this point, w_(64a) is given by the following equation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 366} \right\rbrack & \; \\{w_{64\; a} = \frac{z}{\sqrt{\frac{\sum\limits_{i = 1}^{64}D_{i}^{2}}{64}}}} & ({H2})\end{matrix}$

Therefore, the mapped baseband signal has an average power of z₂.

In the above description, the case equal to (Configuration example R1)is referred to as uniform-64QAM, and other cases are referred to asnon-uniform 64QAM.

The 256QAM mapping method will be described below. FIG. 113 illustratesan arrangement example of 256QAM signal points in the I-Q plane. In FIG.113 , 256 marks “◯” indicate 256QAM signal points, a horizontal axisindicates I, and a vertical axis indicates Q. In FIG. 113 , it isassumed that h₁>0 (h₁ is a real number larger than 0) and h₂>0 (h₂ is areal number larger than 0) and h₃>0 (h₃ is a real number larger than 0)and h₄>0 (h₄ is a real number larger than 0) and h₅>0 (h₅ is a realnumber larger than 0) and h₆>0 (h₆ is a real number larger than 0) andh₇>0 (h₇ is a real number larger than 0),

that {{h₁≠15 and h₂≠15 and h₃≠15 and h₄≠15 and h₅≠15 and h₆≠15 andh₇≠15} holds},

and

that {when {a1 is an integer from 1 to 7 and a2 is an integer from 1 to7 and a3 is an integer from 1 to 7 and a4 is an integer from 1 to 7 anda5 is an integer from 1 to 7 and a6 is an integer from 1 to 7 and a7 isan integer from 1 to 7} holds, when {x is an integer from 1 to 7 and γis an integer from 1 to 7 and x≠y} holds, and when {ax≠ay holds for allthe values x and y}, (h_(a1), h_(a2), h_(a3), h_(a4), h_(a5), h_(a6),h_(a7))≠(1,3,5,7,9,11,13) holds.},and that {{h₁≠h₂ and h₁≠h₃ and h₁≠h₄ and h₁≠h₅ and h₁≠h₆ and h₁≠h₇,and h₂≠h₃ and h₂≠h₄ and h₂≠h₅ and h₂≠h₆ and h₂≠h₇,and h₃≠h₄ and h₃≠h₅ and h₃≠h₆ and h₃≠h₇,and h₄≠h₅ and h₄≠h₆ and h₄≠h₇,and h₅≠h₆ and h₅≠h₇,and h₆≠h₇} hold.}

256 signal points included in 256QAM (indicated by the marks “◯” in FIG.113 ) in the I-Q plane are obtained as follows. (w_(256a) is a realnumber larger than 0)

(15×w_(256a), 15×w_(256a)), (15×w_(256a),h₇×w_(256a)),(15×w_(256a),h₆×w_(256a)), (15×w_(256a), h₅×w_(256a)),(15×w_(256a),h₄×w_(256a)), (15×w_(256a),h₃×w_(256a)),(15×w_(256a),h₂×w_(256a)), (15×w_(256a),h₁×w_(256a)), (15×w_(256a),−15×w_(256a)), (15×w_(256a),−h₇×w_(256a)), (15×w_(256a),−h₆×w_(256a)),(15×w_(256a),−h₅×w_(256a)), (15×w_(256a),−h₄×w_(256a)),(15×w_(256a),−h₃×w_(256a)), (15×w_(256a),−h₂×w_(256a)),(15×w_(256a),−h₁×w_(256a)),(h₇×w_(256a), 15×w_(256a)), (h₇×w_(256a),h₇×w_(256a)),(h₇×w_(256a),h₆×w_(256a)), (h₇×w_(256a), h₅×w_(256a)),(h₇×w_(256a),h₄×w_(256a)), (h₇×w_(256a),h₃×w_(256a)), (h₇×w_(256a),h₂×w_(256a)), (h₇×w_(256a), h₁×w_(256a)), (h₇×w_(256a),−15×w_(256a)),(h₇×w_(256a),−h₇×w_(256a)), (h₇×w_(256a),−h₆×w_(256a)),(h₇×w_(256a),−h₅×w_(256a)), (h₇×w_(256a),−h₄×w_(256a)),(h₇×w_(256a),−h₃×w_(256a)), (h₇×w_(256a),−h₂×w_(256a)),(h₇×w_(256a),−h₁×w_(256a)),(h₆×w_(256a), 15×w_(256a)), (h₆×w_(256a), h₇×w_(256a)), (h₆×w_(256a),h₆×w_(256a)), (h₆×w_(256a), h₅×w_(256a)), (h₆×w_(256a),h₄×w_(256a)),(h₆×w_(256a), h₃×w_(256a)), (h₆×w_(256a), h₂×w_(256a)), (h₆×w_(256a),h₁×w_(256a)), (h₆×w_(256a),−15×w_(256a)), (h₆×w_(256a),−h₇×w_(256a)),(h₆×w_(256a),−h₆×w_(256a)), (h₆×w_(256a),−h₅×w_(256a)),(h₆×w_(256a),−h₄×w_(256a)), (h₆×w_(256a),−h₃×w_(256a)),(h₆×w_(256a),−h₂×w_(256a)), (h₆×w_(256a),−h₁×w_(256a)),(h₅×w_(256a), 15×w_(256a)), (h₅×w_(256a), h₇×w_(256a)), (h₅×w_(256a),h₆×w_(256a)), (h₅×w_(256a), h₅×w_(256a)), (h₅×w_(256a),h₄×w_(256a)),(h₅×w_(256a), h₃×w_(256a)), (h₅×w_(256a), h₂×w_(256a)), (h₅×w_(256a),h₁×w_(256a)), (h₅×w_(256a),−15×w_(256a)), (h₅×w_(256a),−h₇×w_(256a)),(h₅×w_(256a),−h₆×w_(256a)), (h₅×w_(256a),−h₅×w_(256a)),(h₅×w_(256a),−h₄×w_(256a)), (h₅×w_(256a),−h₃×w_(256a)),(h₅×w_(256a),−h₂×w_(256a)), (h₅×w_(256a),−h₁×w_(256a)),(h₄×w_(256a), 15×w_(256a)), (h₄×w_(256a),h₇×w_(256a)),(h₄×w_(256a),h₆×w_(256a)), (h₄×w_(256a), h₅×w_(256a)),(h₄×w_(256a),h₄×w_(256a)), (h₄×w_(256a),h₃×w_(256a)), (h₄×w_(256a),h₂×w_(256a)), (h₄×w_(256a), h₁×w_(256a)), 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At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, b5, b6, and b7. For example, for the bits to betransmitted (b0, b1, b2, b3, b4, b5, b6, b7)=(0,0,0,0,0,0,0,0), the bitsare mapped at signal point 11301 in FIG. 113 , and (I,Q)=(15×w_(256a),15×w_(256a)) is obtained when I is an in-phase component while Q is aquadrature component of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5, b6, b7),in-phase component I and quadrature component Q of the mapped basebandsignal are decided (during 256QAM modulation). FIG. 113 illustrates anexample of a relationship between the set of b0, b1, b2, b3, b4, b5, b6,and b7 (00000000 to 11111111) and the signal point coordinates. Values00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6, and b7are indicated immediately below 256 signal points included in 256QAM(the marks “◯” in FIG. 113 ) (15×w_(256a), 15×w_(256a)),(15×w_(256a),h₇×w_(256a)), (15×w_(256a),h₆×w_(256a)), (15×w_(256a),h₅×w_(256a)), (15×w_(256a), h₄×w_(256a)), (15×w_(256a), h₃×w_(256a)),(15×w_(256a), h₂×w_(256a)), (15×w_(256a),h₁×w_(256a)),

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(h₁×w_(256a),−h₄×w_(256a)),(h₁×w_(256a),−h₃×w_(256a)), (h₁×w_(256a),−h₂×w_(256a)),(h₁×w_(256a),−h₁×w_(256a)),(−15×w_(256a), 15×w_(256a)), (−15×w_(256a),h₇×w_(256a)),(−15×w_(256a),h₆×w_(256a)), (−15×w_(256a), h₅×w_(256a)),(−15×w_(256a),h₄×w_(256a)), (−15×w_(256a),h₃×w_(256a)), (−15×w_(256a),h₂×w_(256a)), (−15×w_(256a), h₁×w_(256a)), (−15×w_(256a),−15×w_(256a)),(−15×w_(256a),−h₇×w_(256a)), (−15×w_(256a),−h₆×w_(256a)),(−15×w_(256a),−h₅×w_(256a)), (−15×w_(256a),−h₄×w_(256a)),(−15×w_(256a),−h₃×w_(256a)), (−15×w_(256a),−h₂×w_(256a)),(−15×w_(256a),−h₁×w_(256a)),(−h₇×w_(256a), 15×w_(256a)), (−h₇×w_(256a),h₇×w_(256a)),(−h₇×w_(256a),h₆×w_(256a)), (−h₇×w_(256a), h₅×w_(256a)),(−h₇×w_(256a),h₄×w_(256a)), (−h₇×w_(256a),h₃×w_(256a)),(−h₇×w_(256a),h₂×w_(256a)), (−h₇×w_(256a),h₁×w_(256a)), (−h₇×w_(256a),−15×w_(256a)), (−h₇×w_(256a),−h₇×w_(256a)), (−h₇×w_(256a),−h₆×w_(256a)),(−h₇×w_(256a),−h₅×w_(256a)), (−h₇×w_(256a),−h₄×w_(256a)),(−h₇×w_(256a),−h₃×w_(256a)), (−h₇×w_(256a),−h₂×w_(256a)),(−h₇×w_(256a),−h₁×w_(256a)),(−h₆×w_(256a), 15×w_(256a)), (−h₆×w_(256a), h₇×w_(256a)), (−h₆×w_(256a),h₆×w_(256a)), (−h₆×w_(256a), h₅×w_(256a)), (−h₆×w_(256a),h₄×w_(256a)),(−h₆×w_(256a),h₃×w_(256a)), (−h₆×w_(256a),h₂×w_(256a)),(−h₆×w_(256a),h₁×w_(256a)), (−h₆×w_(256a), −15×w_(256a)),(−h₆×w_(256a),−h₇×w_(256a)), (−h₆×w_(256a),−h₆×w_(256a)),(−h₆×w_(256a),−h₅×w_(256a)), (−h₆×w_(256a),−h₄×w_(256a)),(−h₆×w_(256a),−h₃×w_(256a)), (−h₆×w_(256a),−h₂×w_(256a)),(−h₆×w_(256a),−h₁×w_(256a)),(−h₅×w_(256a), 15×w_(256a)), (−h₅×w_(256a), h₇×w_(256a)), (−h₅×w_(256a),h₆×w_(256a)), (−h₅×w_(256a), h₅×w_(256a)), (−h₅×w_(256a),h₄×w_(256a)),(−h₅×w_(256a),h₃×w_(256a)), (−h₅×w_(256a),h₂×w_(256a)),(−h₅×w_(256a),h₁×w_(256a)), (−h₅×w_(256a), −15×w_(256a)),(−h₅×w_(256a),−h₇×w_(256a)), (−h₅×w_(256a),−h₆×w_(256a)),(−h₅×w_(256a),−h₅×w_(256a)), (−h₅×w_(256a),−h₄×w_(256a)),(−h₅×w_(256a),−h₃×w_(256a)), (−h₅×w_(256a),−h₂×w_(256a)),(−h₅×w_(256a),−h₁×w_(256a)),(−h₄×w_(256a), 15×w_(256a)), (−h₄×w_(256a),h₇×w_(256a)),(−h₄×w_(256a),h₆×w_(256a)), (−h₄×w_(256a), h₅×w_(256a)),(−h₄×w_(256a),h₄×w_(256a)), (−h₄×w_(256a),h₃×w_(256a)),(−h₄×w_(256a),h₂×w_(256a)), (−h₄×w_(256a),h₁×w_(256a)), (−h₄×w_(256a),−15×w_(256a)), (−h₄×w_(256a),−h₇×w_(256a)), (−h₄×w_(256a),−h₆×w_(256a)),(−h₄×w_(256a),−h₅×w_(256a)), (−h₄×w_(256a),−h₄×w_(256a)),(−h₄×w_(256a),−h₃×w_(256a)), (−h₄×w_(256a),−h₂×w_(256a)),(−h₄×w_(256a),−h₁×w_(256a)),(−h₃×w_(256a), 15×w_(256a)), (−h₃×w_(256a), h₇×w_(256a)), (−h₃×w_(256a),h₆×w_(256a)), (−h₃×w_(256a), h₅×w_(256a)), (−h₃×w_(256a),h₄×w_(256a)),(−h₃×w_(256a),h₃×w_(256a)), (−h₃×w_(256a),h₂×w_(256a)),(−h₃×w_(256a),h₁×w_(256a)), (−h₃×w_(256a), −15×w_(256a)),(−h₃×w_(256a),−h₇×w_(256a)), (−h₃×w_(256a),−h₆×w_(256a)),(−h₃×w_(256a),−h₅×w_(256a)), (−h₃×w_(256a),−h₄×w_(256a)),(−h₃×w_(256a),−h₃×w_(256a)), (−h₃×w_(256a),−h₂×w_(256a)),(−h₃×w_(256a),−h₁×w_(256a)),(−h₂×w_(256a), 15×w_(256a)), (−h₂×w_(256a), h₇×w_(256a)), (−h₂×w_(256a),h₆×w_(256a)), (−h₂×w_(256a), h₅×w_(256a)), (−h₂×w_(256a),h₄×w_(256a)),(−h₂×w_(256a),h₃×w_(256a)), (−h₂×w_(256a),h₂×w_(256a)),(−h₂×w_(256a),h₁×w_(256a)), (−h₂×w_(256a), −15×w_(256a)),(−h₂×w_(256a),−h₇×w_(256a)), (−h₂×w_(256a),−h₆×w_(256a)),(−h₂×w_(256a),−h₅×w_(256a)), (−h₂×w_(256a),−h₄×w_(256a)),(−h₂×w_(256a),−h₃×w_(256a)), (−h₂×w_(256a),−h₂×w_(256a)),(−h₂×w_(256a),−h₁×w_(256a)),(−h₁×w_(256a), 15×w_(256a)), (−h₁×w_(256a),h₇×w_(256a)),(−h₁×w_(256a),h₆×w_(256a)), (−h₁×w_(256a), h₅×w_(256a)),(−h₁×w_(256a),h₄×w_(256a)), (−h₁×w_(256a),h₃×w_(256a)), (−h₁×w_(256a),h₂×w_(256a)), (−h₁×w_(256a), h₁×w_(256a)), (−h₁×w_(256a), −15×w_(256a)),(−h₁×w_(256a),−h₇×w_(256a)), (−h₁×w_(256a),−h₆×w_(256a)),(−h₁×w_(256a),−h₅×w_(256a)), (−h₁×w_(256a),−h₄×w_(256a)),(−h₁×w_(256a),−h₃×w_(256a)), (−h₁×w_(256a),−h₂×w_(256a)),(−h₁×w_(256a),−h₁×w_(256a)). Respective coordinates of the signal points(“◯”) immediately above the values 00000000 to 11111111 of the set ofb0, b1, b2, b3, b4, b5, b6, and b7 in the I-Q plane serve as in-phasecomponent I and quadrature component Q of the mapped baseband signal.The relationship between the set of b0, b1, b2, b3, b4, b5, b6, and b7(00000000 to 11111111) and the signal point coordinates during 256QAMmodulation is not limited to that in FIG. 113 .

256 signal points in FIG. 113 are named as “signal point 1”, “signalpoint 2”, . . . , “signal point 255”, and “signal point 256” (because ofthe presence of 256 signal points, “signal point 1” to “signal point256” exist). In the I-Q plane, Di is a distance between “signal point i”and the origin. At this point, w_(256a) is given by the followingequation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 367} \right\rbrack & \; \\{w_{256\; a} = \frac{z}{\sqrt{\frac{\sum\limits_{i = 1}^{256}D_{i}^{2}}{256}}}} & ({H3})\end{matrix}$

Therefore, the mapped baseband signal has an average power of z₂.

In the above description, the case equal to (Configuration example R1)is referred to as uniform-256QAM, and other cases are referred to asnon-uniform 256QAM.

(Supplement 3)

The bit length adjusting method is described in the first to eleventhexemplary embodiments. The method for applying the bit length adjustingmethods of the first to eleventh exemplary embodiments to the DVBstandard is described in the twelfth exemplary embodiment. The case that16QAM, 64QAM, and 256QAM are applied as the modulation scheme isdescribed in the above exemplary embodiments. A specific mapping methodwith respect to 16QAM, 64QAM, and 256QAM is described in (Configurationexample R1).

A specific mapping method with respect to 16QAM, 64QAM, and 256QAMdifferent from that of (Configuration example R1) and (Supplement 2)will be described below. The following 16QAM, 64QAM, and 256QAM may beapplied to the first to twelfth exemplary embodiments, and the effectsof the first to twelfth exemplary embodiments can also be obtained.

The 16QAM mapping method will be described below. FIG. 114 illustratesan arrangement example of 16QAM signal points in the I-Q plane. In FIG.114 , 16 marks “◯” indicate 16QAM signal points, a horizontal axisindicates I, and a vertical axis indicates Q. In FIG. 114 , it isassumed that f₁>0 (f₁ is a real number larger than 0), f₂>0 (f₂ is areal number larger than 0), f₁≠3, and f₁≠f₂ hold.

In the I-Q plane, 16 signal points included in 16QAM (indicated by themarks “◯” in FIG. 114 ) are obtained as follows. (w_(16b) is a realnumber larger than 0)

(3×w_(16b),3×w_(16b)), (3×w_(16b),f₂×w_(16b)), (3×w_(16b),−f₂×w_(16b)),(3×w_(16b),−3×w_(16b)), (f₁×w_(16b),3×w_(16b)), (f₁×w_(16b),f₂×w_(16b)),(f₁×w_(16b),−f₂×w_(16b)), (f₁×w_(16b),−3×w_(16b)),(−f₁×w_(16b),3×w_(16b)), (−f₁×w_(16b),f₂×w_(16b)), (−f₁×w_(16b),f₂×w_(16b)), (−f₁×w_(16b),−3×w_(16b)), (−3×w_(16b),3×w_(16b)),(−3×w_(16b),f₂×w_(16b)), (−3×w_(16b),−f₂×w_(16b)),(−3×w_(16b),−3×w_(16b))

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, and b3. For example, for the bits to be transmitted (b0, b1, b2,b3)=(0,0,0,0), the bits are mapped at signal point 11401 in FIG. 114 ,and (I,Q)=(3×w_(16b),3×w_(16b)) is obtained when I is an in-phasecomponent while Q is a quadrature component of the mapped basebandsignal.

Based on the bits to be transmitted (b0, b1, b2, b3), in-phase componentI and quadrature component Q of the mapped baseband signal are decided(during 16QAM modulation). FIG. 114 illustrates an example of therelationship between the set of b0, b1, b2, and b3 (0000 to 1111) andthe signal point coordinates. Values 0000 to 1111 of the set of b0, b1,b2, and b3 are indicated immediately below 16 signal points included in16QAM (the marks “◯” in FIG. 114 ) (3×w_(16b),3×w_(16b)),(3×w_(16b),f₂×w_(16b)), (3×w_(16b),−f₂×w_(16b)), (3×w_(16b),−3×w_(16b)),(f₁×w_(16b),3×w_(16b)), (f₁×w_(16b),f₂×w_(16b)),(f₁×w_(16b),−f₂×w_(16b)), (f₁×w_(16b),−3×w_(16b)),(−f₁×w_(16b),3×w_(16b)), (−f₁×w_(16b),f₂×w_(16b)),(−f₁×w_(16b),−f₂×w_(16b)), (−f₁×w_(16b),−3×w_(16b)),(−3×w_(16b),3×w_(16b)), (−3×w_(16b),f₂×w_(16b)),(−3×w_(16b),−f₂×w_(16b)), (−3×w_(16b),−3×w_(16b)). Respectivecoordinates of the signal points (“◯”) immediately above the values 0000to 1111 of the set of b0, b1, b2, and b3 in the I-Q plane serve asin-phase component I and quadrature component Q of the mapped basebandsignal. The relationship between the set of b0, b1, b2, and b3 (0000 to1111) and the signal point coordinates during 16QAM modulation is notlimited to that in FIG. 114 .

16 signal points in FIG. 114 are named as “signal point 1”, “signalpoint 2”, . . . , “signal point 15”, and “signal point 16” (because ofthe presence of 16 signal points, “signal point 1” to “signal point 16”exist). In the I-Q plane, Di is a distance between “signal point i” andthe origin. At this point, w_(16b) is given by the following equation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 368} \right\rbrack & \; \\\begin{matrix}{w_{16b} = \frac{z}{\sqrt{\frac{\sum\limits_{i = 1}^{16}D_{i}^{2}}{16}}}} \\{= \frac{z}{\sqrt{\frac{\begin{matrix}\left( {{\left( {3^{2} + 3^{2}} \right) \times 4} + {\left( {f_{1}^{2} + f_{2}^{2}} \right) \times 4} +} \right. \\\left. {{\left( {f_{1}^{2} + 3^{2}} \right) \times 4} + {\left( {f_{2}^{2} + 3^{2}} \right) \times 4}} \right)\end{matrix}}{16}}}}\end{matrix} & ({H4})\end{matrix}$

Therefore, the mapped baseband signal has an average power of z₂. Theeffect of 16QAM is described later.

The 64QAM mapping method will be described below. FIG. 115 illustratesan arrangement example of 64QAM signal points in the I-Q plane. In FIG.115 , 64 marks “◯” indicate 64QAM signal points, a horizontal axisindicates I, and a vertical axis indicates Q.

In FIG. 115 , g₁>0 (g₁ is a real number larger than 0) and g₂>0 (g₂ is areal number larger than 0) and g₃>0 (g₃ is a real number larger than 0)and g₄>0 (g₄ is a real number larger than 0) and g₅>0 (g₅ is a realnumber larger than 0) and g_(6>0) (g₆ is a real number larger than 0)hold, and

{g₁≠7 and g₂≠7 and g₃≠7 and g₁≠g₂ and g₁≠g₃ and g₂≠g₃}

and

{g₄≠7 and g₅≠7 and g₆≠7 and g₄≠g₅ and g₄≠g₆ and g₅≠g₆}

and

{{g₁≠g₄ or g₂‥g₅ or g₃≠g₆} holds.} hold.

In the I-Q plane, 64 signal points included in 64QAM (indicated by themarks “◯” in FIG. 115 ) are obtained as follows. (w_(64b) is a realnumber larger than 0)

(7×w_(64b),7×w_(64b)), (7×w_(64b),g₆×w_(64b)), (7×w_(64b),g₅×w_(64b)),(7×w_(64b),g₄×w_(64b)), (7×w_(64b),−g₄×w_(64b)),(7×w_(64b),−g₅×w_(64b)), (7×w_(64b),−g₆×w_(64b)), (7×w_(64b),−7×w_(64b))

(g₃×w_(64b),7×w_(64b)), (g₃×w_(64b),g₆×w_(64b)),(g₃×w_(64b),g₅×w_(64b)), (g₃×w_(64b),g₄×w_(64b)),(g₃×w_(64b),−g₄×w_(64b)), (g₃×w_(64b),−g₅×w_(64b)),(g₃×w_(64b),−g₆×w_(64b)), (g₃×w_(64b),−7×w_(64b))

(g₂×w_(64b),7×w_(64b)), (g₂×w_(64b),g₆×w_(64b)),(g₂×w_(64b),g₅×w_(64b)), (g₂×w_(64b),g₄×w_(64b)),(g₂×w_(64b),−g₄×w_(64b)), (g₂×w_(64b),−g₅×w_(64b)),(g₂×w_(64b),−g₆×w_(64b)), (g₂×w_(64b),−7×w_(64b))

(g₁×w_(64b),7×w_(64b)), (g₁×w_(64b),g₆×w_(64b)),(g₁×w_(64b),g₅×w_(64b)), (g₁×w_(64b),g₄×w_(64b)),(g₁×w_(64b),−g₄×w_(64b)), (g₁×w_(64b),−g₅×w_(64b)),(g₁×w_(64b),−g₆×w_(64b)), (g₁×w_(64b),−7×w_(64b))

(−g₁×w_(64b),7×w_(64b)), (−g₁×w_(64b),g₆×w_(64b)),(−g₁×w_(64b),g₅×w_(64b)), (−g₁×w_(64b),g₄×w_(64b)),(−g₁×w_(64b),−g₄×w_(64b)), (−g₁×w_(64b),−g₅×w_(64b)),(−g₁×w_(64b),−g₆×w_(64b)), (−g₁×w_(64b),−7×w_(64b))

(−g₂×w_(64b), 7×w_(64b)), (−g₂×w_(64b),g₆×w_(64b)),(−g₂×w_(64b),g₅×w_(64b)), (−g₂×w_(64b),g₄×w_(64b)), (−g₂×w_(64b),−g₄×w_(64b)), (−g₂×w_(64b),−g₅×w_(64b)), (−g₂×w_(64b),−g₆×w_(64b)),(−g₂×w_(64b),−7×w_(64b))

(−g₃×w_(64b), 7×w_(64b)), (−g₃×w_(64b),g₆×w_(64b)),(−g₃×w_(64b),g₅×w_(64b)), (−g₃×w_(64b),g₄×w_(64b)),(−g₃×w_(64b),−g₄×w_(64b)), (−g₃×w_(64b),−g₅×w_(64b)),(−g₃×w_(64b),−g₆×w_(64b)), (−g₃×w_(64b),−7×w_(64b))

(−7×w_(64b),7×w_(64b)), (−7×w_(64b),g₆×w_(64b)),(−7×w_(64b),g₅×w_(64b)), (−7×w_(64b),g₄×w_(64b)),(−7×w_(64b),−g₄×w_(64b)), (−7×w_(64b),−g₅×w_(64b)),(−7×w_(64b),−g₆×w_(64b)), (−7×w_(64b),−7×w_(64b))

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, for the bits to be transmitted (b0,b1, b2, b3, b4, b5)=(0,0,0,0,0,0), the bits are mapped at signal point11501 in FIG. 115 , and (I,Q)=(7×w_(64b),7×w_(64b)) is obtained when Iis an in-phase component while Q is a quadrature component of the mappedbaseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 115 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to 111111 of theset of b0, b1, b2, b3, b4, and b5 are indicated immediately below 64signal points included in 64QAM (the marks “◯” in FIG. 115 )(7×w_(64b),7×w_(64b)), (7×w_(64b),g₆×w_(64b)), (7×w_(64b),g₅×w_(64b)),(7×w_(64b),g₄×w_(64b)), (7×w_(64b),−g₄×w_(64b)),(7×w_(64b),−g₅×w_(64b)), (7×w_(64b),−g₆×w_(64b)), (7×w_(64b),−7×w_(64b))

(g₃×w_(64b),7×w_(64b)), (g₃×w_(64b),g₆×w_(64b)),(g₃×w_(64b),g₅×w_(64b)), (g₃×w_(64b),g₄×w_(64b)),(g₃×w_(64b),−g₄×w_(64b)), (g₃×w_(64b),−g₅×w_(64b)),(g₃×w_(64b),−g₆×w_(64b)), (g₃×w_(64b),−7×w_(64b))

(g₂×w_(64b),7×w_(64b)), (g₂×w_(64b),g₆×w_(64b)),(g₂×w_(64b),g₅×w_(64b)), (g₂×w_(64b),g₄×w_(64b)),(g₂×w_(64b),−g₄×w_(64b)), (g₂×w_(64b),−g₅×w_(64b)),(g₂×w_(64b),−g₆×w_(64b)), (g₂×w_(64b),−7×w_(64b))

(g₁×w_(64b),7×w_(64b)), (g₁×w_(64b),g₆×w_(64b)),(g₁×w_(64b),g₅×w_(64b)), (g₁×w_(64b),g₄×w_(64b)),(g₁×w_(64b),−g₄×w_(64b)), (g₁×w_(64b),−g₅×w_(64b)),(g₁×w_(64b),−g₆×w_(64b)), (g₁×w_(64b),−7×w_(64b))

(−g₁×w_(64b),7×w_(64b)), (−g₁×w_(64b),g₆×w_(64b)),(−g₁×w_(64b),g₅×w_(64b)), (−g₁×w_(64b),g₄×w_(64b)),(−g₁×w_(64b),−g₄×w_(64b)), (−g₁×w_(64b),−g₅×w_(64b)),(−g₁×w_(64b),−g₆×w_(64b)), (−g₁×w_(64b),−7×w_(64b))

(−g₂×w_(64b),7×w_(64b)), (−g₂×w_(64b),g₆×w_(64b)),(−g₂×w_(64b),g₅×w_(64b)), (−g₂×w_(64b),g₄×w_(64b)), (−g₂×w_(64b),−g₄×w_(64b)), (˜g₂×w_(64b),−g₅×w_(64b)), (˜g₂×w_(64b),−g₆×w_(64b)),(˜g₂×w_(64b),−7×w_(64b))

(−g₃×w_(64b), 7×w_(64b)), (−g₃×w_(64b),g₆×w_(64b)),(−g₃×w_(64b),g₅×w_(64b)), (−g₃×w_(64b),g₄×w_(64b)),(−g₃×w_(64b),−g₄×w_(64b)), (−g₃×w_(64b),−g₅×w_(64b)),(−g₃×w_(64b),−g₆×w_(64b)), (−g₃×w_(64b),−7×w_(64b))

(−7×w_(64b),7×w_(64b)), (−7×w_(64b),g₆×w_(64b)),(−7×w_(64b),g₅×w_(64b)), (−7×w_(64b),g₄×w_(64b)),(−7×w_(64b),−g₄×w_(64b)), (−7×w_(64b),−g₅×w_(64b)),(−7×w_(64b),−g₆×w_(64b)), (−7×w_(64b),−7×w_(64b)). Respectivecoordinates of the signal points (“◯”) immediately above the values000000 to 111111 of the set of b0, b1, b2, b3, b4, and b5 in the I-Qplane serve as in-phase component I and quadrature component Q of themapped baseband signal. The relationship between the set of b0, b1, b2,b3, b4, and b5 (000000 to 111111) and the signal point coordinatesduring 64QAM modulation is not limited to that in FIG. 115 .

64 signal points in FIG. 115 are named as “signal point 1”, “signalpoint 2”, . . . , “signal point 63”, and “signal point 64” (because ofthe presence of 64 signal points, “signal point 1” to “signal point 64”exist). In the I-Q plane, Di is a distance between “signal point i” andthe origin. At this point, w_(64b) is given by the following equation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 369} \right\rbrack & \; \\{w_{64b} = \frac{z}{\sqrt{\frac{\sum\limits_{i = 1}^{64}D_{i}^{2}}{64}}}} & ({H5})\end{matrix}$

Therefore, the mapped baseband signal has an average power of z₂. Theeffect is described later.

The 256QAM mapping method will be described below. FIG. 116 illustratesan arrangement example of 256QAM signal points in the I-Q plane. In FIG.116 , 256 marks “◯” indicate 256QAM signal points, a horizontal axisindicates I, and a vertical axis indicates Q.

In FIG. 116 , h₁>0 (h₁ is a real number larger than 0) and h₂>0 (h₂ is areal number larger than 0) and h₃>0 (h₃ is a real number larger than 0)and h₄>0 (h₄ is a real number larger than 0) and h₅>0 (h₅ is a realnumber larger than 0) and h₆>0 (h₆ is a real number larger than 0) andh₇>0 (h₇ is a real number larger than 0),

and h₈>0 (h₈ is a real number larger than 0) and h₉>0 (h₉ is a realnumber larger than 0) and h₁₀>0 (h₁₀ is a real number larger than 0) andh₁₁>0 (h₁₁ is a real number larger than 0) and h₁₂>0 (h₁₂ is a realnumber larger than 0) and h₁₃>0 (h₁₃ is a real number larger than 0) andh₁₄>0 (h₁₄ is a real number larger than 0),{h₁≠15 and h₂≠15 and h₃≠15 and h₄≠15 and h₅≠15 and h₆≠15 and h₇≠15,and h₁≠h₂ and h₁≠h₃ and h₁≠h₄ and h₁≠h₅ and h₁≠h₆ and h₁≠h₇,and h₂≠h₃ and h₂≠h₄ and h₂≠h₅ and h₂≠h₆ and h₂≠h₇,and h₃≠h₄ and h₃≠h₅ and h₃≠h₆ and h₃≠h₇,and h₄≠h₅ and h₄≠h₆ and h₄≠h₇,and h₅≠h₆ and h₅≠h₇,and h₆≠h₇}and{h₈≠15 and h₉≠15 and h₁₀≠15 and h₁₁≠15 and h₁₂≠15 and h₁₃≠15 and h₁₄≠15,and h₈≠h₉ and h₈≠h₁₀ and h₈≠h₁₁ and h₈≠h₁₂ and h₈≠h₁₃ and h₈≠h₁₄,and h₉≠h₁₀ and h₉≠h₁₁ and h₉≠h₁₂ and h₉≠h₁₃ and h₉≠h₁₄,and h₁₀≠h₁₁ and h₁₀≠h₁₂ and h₁₀≠h₁₃ and h₁₀≠h₁₄,and h₁₁≠h₁₂ and h₁₁≠h₁₃ and h₁₁≠h₁₄,and h₁₂≠h₁₃ and h₁₂≠h₁₄,and h₁₃≠h₁₄}and{h₁≠h₈ or h₂≠h₉ or h₃≠h₁₀ or h₄≠h₁₁ or h₅≠h₁₂ or h₆≠h₁₃ or h₇≠h₁₄ holds}hold.

In the I-Q plane, 256 signal points included in 256QAM (indicated by themarks “◯” in FIG. 116 ) are obtained as follows. (w_(256b) is a realnumber larger than 0)

(15×w_(256b), 15×w_(256b)), (15×w_(256b), h₁₄×w_(256b)),(15×w_(256b),h₁₃×w_(256b)), (15×w_(256b), h₁₂×w_(256b)),(15×w_(256b),h₁₁×w_(256b)), (15×w_(256b),h₁₀×w_(256b)),(15×w_(256b),h₉×w_(256b)), (15×w_(256b),h₈×w_(256b)), (15×w_(256b),−15×w_(256b)), (15×w_(256b),−h₁₄×w_(256b)), (15×w_(256b),−h₁₃×w_(256b)),(15×w_(256b),−h₁₂×w_(256b)), (15×w_(256b),−h₁₁×w_(256b)),(15×w_(256b),−h₁₀×w_(256b)), (15×w_(256b),−h₉×w_(256b)),(15×w_(256b),−h₈×w_(256b)),(h₇×w_(256b), 15×w_(256b)), (h₇×w_(256b), h₁₄×w_(256b)),(h₇×w_(256b),h₁₃×w_(256b)), (h₇×w_(256b),h₁₂×w_(256b)),(h₇×w_(256b),h₁₁×w_(256b)), (h₇×w_(256b),h₁₀×w_(256b)),(h₇×w_(256b),h₉×w_(256b)), (h₇×w_(256b),h₈×w_(256b)),(h₇×w_(256b),−15×w_(256b)), (h₇×w_(256b),−h₁₄×w_(256b)),(h₇×w_(256b),−h₁₃×w_(256b)), (h₇×w_(256b),−h₁₂×w_(256b)),(h₇×w_(256b),−h₁₁×w_(256b)), (h₇×w_(256b),−h₁₀×w_(256b)),(h₇×w_(256b),−h₉×w_(256b)), (h₇×w_(256b),−h₈×w_(256b)),(h₆×w_(256b), 15×w_(256b)), (h₆×w_(256b), h₁₄×w_(256b)),(h₆×w_(256b),h₁₃×w_(256b)), (h₆×w_(256b),h₁₂×w_(256b)),(h₆×w_(256b),h₁₁×w_(256b)), (h₆×w_(256b),h₁₀×w_(256b)),(h₆×w_(256b),h₉×w_(256b)), (h₆×w_(256b),h₈×w_(256b)),(h₆×w_(256b),−15×w_(256b)), (h₆×w_(256b),−h₁₄×w_(256b)),(h₆×w_(256b),−h₁₃×w_(256b)), (h₆×w_(256b),−h₁₂×w_(256b)),(h₆×w_(256b),−h₁₁×w_(256b)), (h₆×w_(256b),−h₁₀×w_(256b)),(h₆×w_(256b),−h₉×w_(256b)), (h₆×w_(256b),−h₈×w_(256b)),(h₅×w_(256b), 15×w_(256b)), (h₅×w_(256b), h₁₄×w_(256b)),(h₅×w_(256b),h₁₃×w_(256b)), (h₅×w_(256b),h₁₂×w_(256b)),(h₅×w_(256b),h₁₁×w_(256b)), (h₅×w_(256b),h₁₀×w_(256b)),(h₅×w_(256b),h₉×w_(256b)), (h₅×w_(256b),h₈×w_(256b)),(h₅×w_(256b),−15×w_(256b)), (h₅×w_(256b),−h₁₄×w_(256b)),(h₅×w_(256b),−h₁₃×w_(256b)), (h₅×w_(256b),−h₁₂×w_(256b)),(h₅×w_(256b),−h₁₁×w_(256b)), (h₅×w_(256b),−h₁₀×w_(256b)),(h₅×w_(256b),−h₉×w_(256b)), (h₅×w_(256b),−h₈×w_(256b)),(h₄×w_(256b), 15×w_(256b)), (h₄×w_(256b), h₁₄×w_(256b)),(h₄×w_(256b),h₁₃×w_(256b)), (h₄×w_(256b),h₁₂×w_(256b)),(h₄×w_(256b),h₁₁×w_(256b)), (h₄×w_(256b),h₁₀×w_(256b)),(h₄×w_(256b),h₉×w_(256b)), (h₄×w_(256b),h₈×w_(256b)),(h₄×w_(256b),−15×w_(256b)), (h₄×w_(256b),−h₁₄×w_(256b)),(h₄×w_(256b),−h₁₃×w_(256b)), (h₄×w_(256b),−h₁₂×w_(256b)),(h₄×w_(256b),−h₁₁×w_(256b)), (h₄×w_(256b),−h₁₀×w_(256b)),(h₄×w_(256b),−h₉×w_(256b)), (h₄×w_(256b),−h₈×w_(256b)),(h₃×w_(256b), 15×w_(256b)), (h₃×w_(256b), h₁₄×w_(256b)),(h₃×w_(256b),h₁₃×w_(256b)), (h₃×w_(256b),h₁₂×w_(256b)),(h₃×w_(256b),h₁₁×w_(256b)), (h₃×w_(256b),h₁₀×w_(256b)),(h₃×w_(256b),h₉×w_(256b)), (h₃×w_(256b),h₈×w_(256b)),(h₃×w_(256b),−15×w_(256b)), (h₃×w_(256b),−h₁₄×w_(256b)),(h₃×w_(256b),−h₁₃×w_(256b)), (h₃×w_(256b),−h₁₂×w_(256b)),(h₃×w_(256b),−h₁₁×w_(256b)), (h₃×w_(256b),−h₁₀×w_(256b)),(h₃×w_(256b),−h₉×w_(256b)), (h₃×w_(256b),−h₈×w_(256b)),(h₂×w_(256b), 15×w_(256b)), (h₂×w_(256b), h₁₄×w_(256b)),(h₂×w_(256b),h₁₃×w_(256b)), (h₂×w_(256b),h₁₂×w_(256b)),(h₂×w_(256b),h₁₁×w_(256b)), (h₂×w_(256b),h₁₀×w_(256b)),(h₂×w_(256b),h₉×w_(256b)), (h₂×w_(256b),h₈×w_(256b)),(h₂×w_(256b),−15×w_(256b)), (h₂×w_(256b),−h₁₄×w_(256b)),(h₂×w_(256b),−h₁₃×w_(256b)), (h₂×w_(256b),−h₁₂×w_(256b)),(h₂×w_(256b),−h₁₁×w_(256b)), (h₂×w_(256b),−h₁₀×w_(256b)),(h₂×w_(256b),−h₉×w_(256b)), (h₂×w_(256b),−h₈×w_(256b)),(h₁×w_(256b),15×w_(256b)), (h₁×w_(256b),h₁₄×w_(256b)),(h₁×w_(256b),h₁₃×w_(256b)), (h₁×w_(256b),h₁₂×w_(256b)),(h₁×w_(256b),h₁₁×w_(256b)), (h₁×w_(256b),h₁₀×w_(256b)),(h₁×w_(256b),h₉×w_(256b)), (h₁×w_(256b),h₈×w_(256b)),(h₁×w_(256b),−15×w_(256b)), (h₁×w_(256b),−h₁₄×w_(256b)),(h₁×w_(256b),−h₁₃×w_(256b)), (h₁×w_(256b),−h₁₂×w_(256b)),(h₁×w_(256b),−h₁₁×w_(256b)), (h₁×w_(256b),−h₁₀×w_(256b)),(h₁×w_(256b),−h₉×w_(256b)), (h₁×w_(256b),−h₈×w_(256b)),(−15×w_(256b), 15×w_(256b)), (−15×w_(256b),h₁₄×w_(256b)),(−15×w_(256b),h₁₃×w_(256b)), (−15×w_(256b), h₁₂×w_(256b)),(−15×w_(256b),h₁₁×w_(256b)), (−15×w_(256b),h₁₀×w_(256b)),(−15×w_(256b),h₉×w_(256b)), (−15×w_(256b),h₈×w_(256b)),(−15×w_(256b),−15×w_(256b)), (−15×w_(256b),−h₁₄×w_(256b)),(−15×w_(256b),−h₁₃×w_(256b)), (−15×w_(256b),−h₁₂×w_(256b)),(−15×w_(256b),−h₁₁×w_(256b)), (−15×w_(256b),−h₁₀×w_(256b)),(−15×w_(256b),−h₉×w_(256b)), (−15×w_(256b),−h₈×w_(256b)),(−h₇×w_(256b),15×w_(256b)), (−h₇×w_(256b), h₁₄×w_(256b)), (−h₇×w_(256b),h₁₃×w_(256b)), (−h₇×w_(256b), h₁₂×w_(256b)),(−h₇×w_(256b),h₁₁×w_(256b)), (−h₇×w_(256b),h₁₀×w_(256b)),(−h₇×w_(256b),h₉×w_(256b)), (−h₇×w_(256b),h₈×w_(256b)), (−h₇×w_(256b),−15×w_(256b)), (−h₇×w_(256b),−h₁₄×w_(256b)),(−h₇×w_(256b),−h₁₃×w_(256b)), (−h₇×w_(256b),−h₁₂×w_(256b)),(−h₇×w_(256b),−h₁₁×w_(256b)), (−h₇×w_(256b),−h₁₀×w_(256b)),(−h₇×w_(256b),−h₉×w_(256b)), (−h₇×w_(256b),−h₈×w_(256b)),(−h₆×w_(256b), 15×w_(256b)), (−h₆×w_(256b), h₁₄×w_(256b)),(−h₆×w_(256b), h₁₃×w_(256b)), (−h₆×w_(256b), h₁₂×w_(256b)),(−h₆×w_(256b),h₁₁×w_(256b)), (−h₆×w_(256b),h₁₀×w_(256b)),(−h₆×w_(256b),h₉×w_(256b)), (−h₆×w_(256b),h₈×w_(256b)), (−h₆×w_(256b),−15×w_(256b)), (−h₆×w_(256b),−h₁₄×w_(256b)),(−h₆×w_(256b),−h₁₃×w_(256b)), (−h₆×w_(256b),−h₁₂×w_(256b)),(−h₆×w_(256b),−h₁₁×w_(256b)), (−h₆×w_(256b),−h₁₀×w_(256b)),(−h₆×w_(256b),−h₉×w_(256b)), (−h₆×w_(256b),−h₈×w_(256b)),(−h₅×w_(256b), 15×w_(256b)), (−h₅×w_(256b), h₁₄×w_(256b)),(−h₅×w_(256b), h₁₃×w_(256b)), (−h₅×w_(256b), h₁₂×w_(256b)),(−h₅×w_(256b),h₁₁×w_(256b)), (−h₅×w_(256b),h₁₀×w_(256b)),(−h₅×w_(256b),h₉×w_(256b)), (−h₅×w_(256b),h₈×w_(256b)),(−h₅×w_(256b),−15×w_(256b)), (−h₅×w_(256b),−h₁₄×w_(256b)),(−h₅×w_(256b),−h₁₃×w_(256b)), (−h₅×w_(256b),−h₁₂×w_(256b)),(−h₅×w_(256b),−h₁₁×w_(256b)), (−h₅×w_(256b),−h₁₀×w_(256b)),(−h₅×w_(256b),−h₉×w_(256b)), (−h₅×w_(256b),−h₈×w_(256b)),(−h₄×w_(256b), 15×w_(256b)), (−h₄×w_(256b), h₁₄×w_(256b)),(−h₄×w_(256b), h₁₃×w_(256b)), (−h₄×w_(256b), h₁₂×w_(256b)),(−h₄×w_(256b),h₁₁×w_(256b)), (−h₄×w_(256b),h₁₀×w_(256b)),(−h₄×w_(256b),h₉×w_(256b)), (−h₄×w_(256b),h₈×w_(256b)), (−h₄×w_(256b),−15×w_(256b)), (−h₄×w_(256b),−h₁₄×w_(256b)),(−h₄×w_(256b),−h₁₃×w_(256b)), (−h₄×w_(256b),−h₁₂×w_(256b)),(−h₄×w_(256b),−h₁₁×w_(256b)), (−h₄×w_(256b),−h₁₀×w_(256b)),(−h₄×w_(256b),−h₉×w_(256b)), (−h₄×w_(256b),−h₈×w_(256b)),(−h₃×w_(256b), 15×w_(256b)), (−h₃×w_(256b), h₁₄×w_(256b)),(−h₃×w_(256b), h₁₃×w_(256b)), (−h₃×w_(256b), h₁₂×w_(256b)),(−h₃×w_(256b),h₁₁×w_(256b)), (−h₃×w_(256b),h₁₀×w_(256b)),(−h₃×w_(256b),h₉×w_(256b)), (−h₃×w_(256b),h₈×w_(256b)), (−h₃×w_(256b),−15×w_(256b)), (−h₃×w_(256b),−h₁₄×w_(256b)),(−h₃×w_(256b),−h₁₃×w_(256b)), (−h₃×w_(256b),−h₁₂×w_(256b)),(−h₃×w_(256b),−h₁₁×w_(256b)), (−h₃×w_(256b),−h₁₀×w_(256b)),(−h₃×w_(256b),−h₉×w_(256b)), (−h₃×w_(256b),−h₈×w_(256b)),(−h₂×w_(256b), 15×w_(256b)), (−h₂×w_(256b), h₁₄×w_(256b)),(−h₂×w_(256b), h₁₃×w_(256b)), (−h₂×w_(256b), h₁₂×w_(256b)),(−h₂×w_(256b),h₁₁×w_(256b)), (−h₂×w_(256b),h₁₀×w_(256b)),(−h₂×w_(256b),h₉×w_(256b)), (−h₂×w_(256b),h₈×w_(256b)), (−h₂×w_(256b),−15×w_(256b)), (−h₂×w_(256b),−h₁₄×w_(256b)),(−h₂×w_(256b),−h₁₃×w_(256b)), (−h₂×w_(256b),−h₁₂×w_(256b)),(−h₂×w_(256b),−h₁₁×w_(256b)), (−h₂×w_(256b),−h₁₀×w_(256b)),(−h₂×w_(256b),−h₉×w_(256b)), (−h₂×w_(256b),−h₈×w_(256b)),(−h₁×w_(256b), 15×w_(256b)), (−h₁×w_(256b), h₁₄×w_(256b)),(−h₁×w_(256b), h₁₃×w_(256b)), (−h₁×w_(256b), h₁₂×w_(256b)),(−h₁×w_(256b),h₁₁×w_(256b)), (−h₁×w_(256b),h₁₀×w_(256b)),(−h₁×w_(256b),h₉×w_(256b)), (−h₁×w_(256b),h₈×w_(256b)), (−h₁×w_(256b),−15×w_(256b)), (−h₁×w_(256b),−h₁₄×w_(256b)),(−h₁×w_(256b),−h₁₃×w_(256b)), (−h₁₁×w_(256b),−h₁₂×w_(256b)),(−h₁×w_(256b),−h₁₁×w_(256b)), (−h₁×w_(256b),−h₁₀×w_(256b)),(−h₁×w_(256b),−h₉×w_(256b)), (−h₁×w_(256b),−h₈×w_(256b))

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, b5, b6, and b7. For example, for the bits to betransmitted (b0, b1, b2, b3, b4, b5, b6, b7)=(0,0,0,0,0,0,0,0), the bitsare mapped at signal point 11601 in FIG. 116 , and (I,Q)=(15×w_(256b),15×w_(256b)) is obtained when I is an in-phase component while Q is aquadrature component of the mapped baseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5, b6, b7),in-phase component I and quadrature component Q of the mapped basebandsignal are decided (during 256QAM modulation). FIG. 116 illustrates anexample of a relationship between the set of b0, b1, b2, b3, b4, b5, b6,and b7 (00000000 to 11111111) and the signal point coordinates. Values00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6, and b7are indicated immediately below 256 signal points included in 256QAM(the marks “◯” in FIG. 116 ) (15×w_(256b), 15×w_(256b)), (15×w_(256b),h₁₄×w_(256b)), (15×w_(256b),h₁₃×w_(256b)), (15×w_(256b), h₁₂×w_(256b)),(15×w_(256b),h₁₁×w_(256b)), (15×w_(256b),h₁₀×w_(256b)),(15×w_(256b),h₉×w_(256b)), (15×w_(256b),h₈×w_(256b)),

(15×w_(256b), −15×w_(256b)), (15×w_(256b),−h₁₄×w_(256b)),(15×w_(256b),−h₁₃×w_(256b)), (15×w_(256b),−h₁₂×w_(256b)),(15×w_(256b),−h₁₁×w_(256b)), (15×w_(256b),−h₁₀×w_(256b)),(15×w_(256b),−h₉×w_(256b)), (15×w_(256b),−h₈×w_(256b)),

(h₇×w_(256b), 15×w_(256b)), (h₇×w_(256b), h₁₄×w_(256b)),(h₇×w_(256b),h₁₃×w_(256b)), (h₇×w_(256b),h₁₂×w_(256b)),(h₇×w_(256b),h₁₁×w_(256b)), (h₇×w_(256b),h₁₀×w_(256b)),(h₇×w_(256b),h₉×w_(256b)), (h₇×w_(256b),h₈×w_(256b)),(h₇×w_(256b),−15×w_(256b)), (h₇×w_(256b),−h₁₄×w_(256b)),(h₇×w_(256b),−h₁₃×w_(256b)), (h₇×w_(256b),−h₁₂×w_(256b)),(h₇×w_(256b),−h₁₁×w_(256b)), (h₇×w_(256b),−h₁₀×w_(256b)),(h₇×w_(256b),−h₉×w_(256b)), (h₇×w_(256b),−h₈×w_(256b)),(h₆×w_(256b), 15×w_(256b)), (h₆×w_(256b), h₁₄×w_(256b)),(h₆×w_(256b),h₁₃×w_(256b)), (h₆×w_(256b),h₁₂×w_(256b)),(h₆×w_(256b),h₁₁×w_(256b)), (h₆×w_(256b),h₁₀×w_(256b)),(h₆×w_(256b),h₉×w_(256b)), (h₆×w_(256b),h₈×w_(256b)),(h₆×w_(256b),−15×w_(256b)), (h₆×w_(256b),−h₁₄×w_(256b)),(h₆×w_(256b),−h₁₃×w_(256b)), (h₆×w_(256b),−h₁₂×w_(256b)),(h₆×w_(256b),−h₁₁×w_(256b)), (h₆×w_(256b),−h₁₀×w_(256b)),(h₆×w_(256b),−h₉×w_(256b)), (h₆×w_(256b),−h₈×w_(256b)),(h₅×w_(256b), 15×w_(256b)), (h₅×w_(256b), h₁₄×w_(256b)),(h₅×w_(256b),h₁₃×w_(256b)), (h₅×w_(256b),h₁₂×w_(256b)),(h₅×w_(256b),h₁₁×w_(256b)), (h₅×w_(256b),h₁₀×w_(256b)),(h₅×w_(256b),h₉×w_(256b)), (h₅×w_(256b),h₈×w_(256b)),(h₅×w_(256b),−15×w_(256b)), (h₅×w_(256b),−h₁₄×w_(256b)),(h₅×w_(256b),−h₁₃×w_(256b)), (h₅×w_(256b),−h₁₂×w_(256b)),(h₅×w_(256b),−h₁₁×w_(256b)), (h₅×w_(256b),−h₁₀×w_(256b)),(h₅×w_(256b),−h₉×w_(256b)), (h₅×w_(256b),−h₈×w_(256b)),(h₄×w_(256b), 15×w_(256b)), (h₄×w_(256b), h₁₄×w_(256b)),(h₄×w_(256b),h₁₃×w_(256b)), (h₄×w_(256b),h₁₂×w_(256b)),(h₄×w_(256b),h₁₁×w_(256b)), (h₄×w_(256b),h₁₀×w_(256b)),(h₄×w_(256b),h₉×w_(256b)), (h₄×w_(256b),h₈×w_(256b)),(h₄×w_(256b),−15×w_(256b)), (h₄×w_(256b),−h₁₄×w_(256b)),(h₄×w_(256b),−h₁₃×w_(256b)), (h₄×w_(256b),−h₁₂×w_(256b)),(h₄×w_(256b),−h₁₁×w_(256b)), (h₄×w_(256b),−h₁₀×w_(256b)),(h₄×w_(256b),−h₉×w_(256b)), (h₄×w_(256b),−h₈×w_(256b)),(h₃×w_(256b), 15×w_(256b)), (h₃×w_(256b), h₁₄×w_(256b)),(h₃×w_(256b),h₁₃×w_(256b)), (h₃×w_(256b),h₁₂×w_(256b)),(h₃×w_(256b),h₁₁×w_(256b)), (h₃×w_(256b),h₁₀×w_(256b)),(h₃×w_(256b),h₉×w_(256b)), (h₃×w_(256b),h₈×w_(256b)),(h₃×w_(256b),−15×w_(256b)), (h₃×w_(256b),−h₁₄×w_(256b)),(h₃×w_(256b),−h₁₃×w_(256b)), (h₃×w_(256b),−h₁₂×w_(256b)),(h₃×w_(256b),−h₁₁×w_(256b)), (h₃×w_(256b),−h₁₀×w_(256b)),(h₃×w_(256b),−h₉×w_(256b)), (h₃×w_(256b),−h₈×w_(256b)),(h₂×w_(256b), 15×w_(256b)), (h₂×w_(256b), h₁₄×w_(256b)),(h₂×w_(256b),h₁₃×w_(256b)), (h₂×w_(256b),h₁₂×w_(256b)),(h₂×w_(256b),h₁₁×w_(256b)), (h₂×w_(256b),h₁₀×w_(256b)),(h₂×w_(256b),h₉×w_(256b)), (h₂×w_(256b),h₈×w_(256b)),(h₂×w_(256b),−15×w_(256b)), (h₂×w_(256b),−h₁₄×w_(256b)),(h₂×w_(256b),−h₁₃×w_(256b)), (h₂×w_(256b),−h₁₂×w_(256b)),(h₂×w_(256b),−h₁₁×w_(256b)), (h₂×w_(256b),−h₁₀×w_(256b)),(h₂×w_(256b),−h₉×w_(256b)), (h₂×w_(256b),−h₈×w_(256b)),(h₁×w_(256b), 15×w_(256b)), (h₁×w_(256b),h₁₄×w_(256b)),(h₁×w_(256b),h₁₃×w_(256b)), (h₁×w_(256b),h₁₂×w_(256b)),(h₁×w_(256b),h₁₁×w_(256b)), (h₁×w_(256b),h₁₀×w_(256b)),(h₁×w_(256b),h₉×w_(256b)), (h₁×w_(256b),h₈×w_(256b)),(h₁×w_(256b),−15×w_(256b)), (h₁×w_(256b),−h₁₄×w_(256b)),(h₁×w_(256b),−h₁₃×w_(256b)), (h₁×w_(256b),−h₁₂×w_(256b)),(h₁×w_(256b),−h₁₁×w_(256b)), (h₁×w_(256b),−h₁₀×w_(256b)),(h₁×w_(256b),−h₉×w_(256b)), (h₁×w_(256b),−h₈×w_(256b)),(−15×w_(256b), 15×w_(256b)), (−15×w_(256b),h₁₄×w_(256b)),(−15×w_(256b),h₁₃×w_(256b)), (−15×w_(256b), h₁₂×w_(256b)),(−15×w_(256b),h₁₁×w_(256b)), (−15×w_(256b),h₁₀×w_(256b)),(−15×w_(256b),h₉×w_(256b)), (−15×w_(256b), h₈×w_(256b)),(−15×w_(256b),−15×w_(256b)), (−15×w_(256b),−h₁₄×w_(256b)),(−15×w_(256b),−h₁₃×w_(256b)), (−15×w_(256b),−h₁₂×w_(256b)),(−15×w_(256b),−h₁₁×w_(256b)), (−15×w_(256b),−h₁₀×w_(256b)),(−15×w_(256b),−h₉×w_(256b)), (−15×w_(256b),−h₈×w_(256b)),(−h₇×w_(256b), 15×w_(256b)), (−h₇×w_(256b), h₁₄×w_(256b)),(−h₇×w_(256b), h₁₃×w_(256b)), (−h₇×w_(256b), h₁₂×w_(256b)),(−h₇×w_(256b),h₁₁×w_(256b)), (−h₇×w_(256b),h₁₀×w_(256b)),(−h₇×w_(256b),h₉×w_(256b)), (−h₇×w_(256b),h₈×w_(256b)), (−h₇×w_(256b),−15×w_(256b)), (−h₇×w_(256b),−h₁₄×w_(256b)),(−h₇×w_(256b),−h₁₃×w_(256b)), (−h₇×w_(256b),−h₁₂×w_(256b)),(−h₇×w_(256b),−h₁₁×w_(256b)), (−h₇×w_(256b),−h₁₀×w_(256b)),(−h₇×w_(256b),−h₉×w_(256b)), (−h₇×w_(256b),−h₈×w_(256b)),(−h₆×w_(256b), 15×w_(256b)), (−h₆×w_(256b), h₁₄×w_(256b)),(−h₆×w_(256b), h₁₃×w_(256b)), (−h₆×w_(256b), h₁₂×w_(256b)),(−h₆×w_(256b),h₁₁×w_(256b)), (−h₆×w_(256b),h₁₀×w_(256b)),(−h₆×w_(256b),h₉×w_(256b)), (−h₆×w_(256b),h₈×w_(256b)), (−h₆×w_(256b),−15×w_(256b)), (−h₆×w_(256b),−h₁₄×w_(256b)),(−h₆×w_(256b),−h₁₃×w_(256b)), (−h₆×w_(256b),−h₁₂×w_(256b)),(−h₆×w_(256b),−h₁₁×w_(256b)), (−h₆×w_(256b),−h₁₀×w_(256b)),(−h₆×w_(256b),−h₉×w_(256b)), (−h₆×w_(256b),−h₈×w_(256b)),(−h₅×w_(256b), 15×w_(256b)), (−h₅×w_(256b), h₁₄×w_(256b)),(−h₅×w_(256b), h₁₃×w_(256b)), (−h₅×w_(256b), h₁₂×w_(256b)),(−h₅×w_(256b),h₁₁×w_(256b)), (−h₅×w_(256b),h₁₀×w_(256b)),(−h₅×w_(256b),h₉×w_(256b)), (−h₅×w_(256b),h₈×w_(256b)), (−h₅×w_(256b),−15×w_(256b)), (−h₅×w_(256b),−h₁₄×w_(256b)),(−h₅×w_(256b),−h₁₃×w_(256b)), (−h₅×w_(256b),−h₁₂×w_(256b)),(−h₅×w_(256b),−h₁₁×w_(256b)), (−h₅×w_(256b),−h₁₀×w_(256b)),(−h₅×w_(256b),−h₉×w_(256b)), (−h₅×w_(256b),−h₈×w_(256b)),(−h₄×w_(256b), 15×w_(256b)), (−h₄×w_(256b), h₁₄×w_(256b)),(−h₄×w_(256b), h₁₃×w_(256b)), (−h₄×w_(256b), h₁₂×w_(256b)),(−h₄×w_(256b),h₁₁×w_(256b)), (−h₄×w_(256b),h₁₀×w_(256b)),(−h₄×w_(256b),h₉×w_(256b)), (−h₄×w_(256b),h₈×w_(256b)), (−h₄×w_(256b),−15×w_(256b)), (−h₄×w_(256b),−h₁₄×w_(256b)),(−h₄×w_(256b),−h₁₃×w_(256b)), (−h₄×w_(256b),−h₁₂×w_(256b)),(−h₄×w_(256b),−h₁₁×w_(256b)), (−h₄×w_(256b),−h₁₀×w_(256b)),(−h₄×w_(256b),−h₉×w_(256b)), (−h₄×w_(256b),−h₈×w_(256b)),(−h₃×w_(256b), 15×w_(256b)), (−h₃×w_(256b), h₁₄×w_(256b)),(−h₃×w_(256b), h₁₃×w_(256b)), (−h₃×w_(256b), h₁₂×w_(256b)),(−h₃×w_(256b),h₁₁×w_(256b)), (−h₃×w_(256b),h₁₀×w_(256b)),(−h₃×w_(256b),h₉×w_(256b)), (−h₃×w_(256b),h₈×w_(256b)), (−h₃×w_(256b),−15×w_(256b)), (−h₃×w_(256b),−h₁₄×w_(256b)),(−h₃×w_(256b),−h₁₃×w_(256b)), (−h₃×w_(256b),−h₁₂×w_(256b)),(−h₁₃×w_(256b),−h₁₁×w_(256b)), (−h₃×w_(256b),−h₁₀×w_(256b)),(−h₃×w_(256b),−h₉×w_(256b)), (−h₃×w_(256b),−h₈×w_(256b)),(−h₂×w_(256b), 15×w_(256b)), (−h₂×w_(256b), h₁₄×w_(256b)),(−h₂×w_(256b), h₁₃×w_(256b)), (−h₂×w_(256b), h₁₂×w_(256b)),(−h₂×w_(256b),h₁₁×w_(256b)), (−h₂×w_(256b),h₁₀×w_(256b)),(−h₂×w_(256b),h₉×w_(256b)), (−h₂×w_(256b),h₈×w_(256b)), (−h₂×w_(256b),−15×w_(256b)), (−h₂×w_(256b),−h₁₄×w_(256b)),(−h₂×w_(256b),−h₁₃×w_(256b)), (−h₂×w_(256b),−h₁₂×w_(256b)),(−h₂×w_(256b),−h₁₁×w_(256b)), (−h₂×w_(256b),−h₁₀×w_(256b)),(−h₂×w_(256b),−h₉×w_(256b)), (−h₂×w_(256b),−h₈×w_(256b)),(−h₁×w_(256b), 15×w_(256b)), (−h₁×w_(256b), h₁₄×w_(256b)),(−h₁×w_(256b), h₁₃×w_(256b)), (−h₁×w_(256b), h₁₂×w_(256b)),(−h₁×w_(256b),h₁₁×w_(256b)), (−h₁×w_(256b),h₁₀×w_(256b)),(−h₁×w_(256b),h₉×w_(256b)), (−h₁×w_(256b),h₈×w_(256b)), (−h₁×w_(256b),−15×w_(256b)), (−h₁×w_(256b),−h₁₄×w_(256b)),(−h₁×w_(256b),−h₁₃×w_(256b)), (−h₁×w_(256b),−h₁₂×w_(256b)),(−h₁×w_(256b),−h₁₁×w_(256b)), (−h₁×w_(256b),−h₁₀×w_(256b)),(−h₁×w_(256b),−h₉×w_(256b)), (−h₁×w_(256b),−h₈×w_(256b)). Respectivecoordinates of the signal points (“◯”) immediately above the values00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6, and b7 inthe I-Q plane serve as in-phase component I and quadrature component Qof the mapped baseband signal.The relationship between the set of b0, b1, b2, b3, b4, b5, b6, and b7(00000000 to 11111111) and the signal point coordinates during 256QAMmodulation is not limited to that in FIG. 116 .

256 signal points in FIG. 116 are named as “signal point 1”, “signalpoint 2”, . . . , “signal point 255”, and “signal point 256” (because ofthe presence of 256 signal points, “signal point 1” to “signal point256” exist). In the I-Q plane, Di is a distance between “signal point i”and the origin. At this point, w_(256b) is given by the followingequation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 370} \right\rbrack & \; \\{w_{256\; b} = \frac{z}{\sqrt{\frac{\sum\limits_{i = 1}^{256}D_{i}^{2}}{256}}}} & ({H6})\end{matrix}$

Therefore, the mapped baseband signal has an average power of z₂. Theeffect is described later.

The effect of the use of QAM will be described below.

First, the configurations of the transmitter and receiver will bedescribed.

FIG. 117 illustrates a configuration example of the transmitter.Information 11701 is input to error correction encoder 11702, and errorcorrection encoder 11702 performs the error correction coding on theLDPC code or a turbo code, and outputs error-correction-coded data11703.

Error-correction-coded data 11703 is input to interleaver 11704, andinterleaver 11704 performs the data rearrangement, and outputs theinterleaved data 11705.

Interleaved data 11705 is input to mapper 11706, and mapper 11706performs the mapping based on the modulation scheme set with thetransmitter, and outputs quadrature baseband signal (in-phase componentI and quadrature component Q) 11707.

Quadrature baseband signal 11707 is input to radio section 11708, andradio section 11708 performs the pieces of processing such as thequadrature modulation, the frequency conversion, and the amplification,and outputs transmitted signal 11709. Transmitted signal 11709 is outputas a radio wave from antenna 11710.

FIG. 118 illustrates an example of the configuration of the receiverthat receives the modulated signal transmitted from the transmitter inFIG. 117 .

Received signal 11802 received with antenna 11801 is input to radiosection 11803, and radio section 11803 performs the pieces of processingsuch as the frequency conversion and the quadrature demodulation, andoutputs quadrature baseband signal 11804.

Quadrature baseband signal 11804 is input to demapper 11805, anddemapper 11805 performs the frequency offset estimation and removal andthe estimation of the channel variation (transmission path variation),estimates each bit of the data symbol, for example, the log-likelihoodratio, and outputs log-likelihood ratio signal 11806.

Log-likelihood ratio signal 11806 is input to deinterleaver 11807, anddeinterleaver 11807 performs the rearrangement, and outputsdeinterleaved log-likelihood ratio signal 11808.

Deinterleaved log-likelihood ratio signal 11808 is input to decoder11809, and decoder 11809 decodes the error correction code, and outputsreceived data 11810.

The effect will be described below with 16QAM as an example. Thefollowing two cases (<16QAM #1> and <16QAM #2>) are compared to eachother.

<16QAM #1>16QAM #1 is 16QAM described in (Supplement 2), and FIG. 111illustrates the arrangement of the signal points in the I-Q plane.

<16QAM #2> FIG. 114 illustrates the arrangement of the signal points inthe I-Q plane, and f₁>0 (f₁ is a real number larger than 0), f₂>0 (f₂ isa real number larger than 0), f₁≠3, f₂≠3, and f₁≠f₂ hold as describedabove.

As described above, four bits of b0, b1, b2, and b3 are transmitted in16QAM. For <16QAM #1>, in the receiver, the four bits are divided intotwo high-quality bits and two low-quality bits in the case that thelog-likelihood ratio of each bit is obtained. On the other hand, for<16QAM #2>, depending on the conditions of f₁>0 (f₁ is a real numberlarger than 0) and f₂>0 (f₂ is a real number larger than 0), f₁≠3, f₁≠3,and f₁≠f₂, the four bits are divided into two high-quality bits, oneintermediate-quality bit, and one low-quality bit. Thus, the qualitydistribution of the 4 bits depends on the <16QAM #1> and <16QAM #2>. Atthis point, in the case that decoder 11809 in FIG. 118 decodes the errorcorrection code, depending on the error correction code used, thereceiver has a higher possibility of obtaining the high data receptionquality using<16QAM #2>.

In the case that the arrangement of the signal points are arranged inthe I-Q plane as illustrated in FIG. 115 for 64QAM, similarly thereceiver has the higher possibility of obtaining the high data receptionquality. At this point, it is necessary to satisfy the followingconditions. That is, “g₁>0 (g₁ is a real number larger than 0) andg_(2>0) (g₂ is a real number larger than 0) and g₃>0 (g₃ is a realnumber larger than 0) and g₄>0 (g₄ is a real number larger than 0) andg₅>0 (g₅ is a real number larger than 0) and g₆>0 (g₆ is a real numberlarger than 0),

{g₁≠7, g₂≠7, g₃≠7, g₁≠g₂, g₁≠g₃, and g₂≠g₃}

and

{g₄≠7 and g₅≠7 and g₆≠7 and g₄≠g₅ and g₄≠g₆ and g₅≠g₆}

and

{g₁≠g₄ or g₂≠g₅ or g₃≠g₆ holds} hold.”, which necessary point differsfrom that in the arrangement of the signal points of (Supplement 2).

Similarly, in the case that the arrangement of the signal points arearranged in the I-Q plane as illustrated in FIG. 116 for 256QAM,similarly the receiver has the higher possibility of obtaining the highdata reception quality. At this point, it is necessary to satisfy thefollowing conditions. That is, “h₁>0 (h₁ is a real number larger than 0)and h₂>0 (h₂ is a real number larger than 0) and h₃>0 (h₃ is a realnumber larger than 0) and h₄>0 (h₄ is a real number larger than 0) andh₅>0 (h₅ is a real number larger than 0) and h₆>0 (h₆ is a real numberlarger than 0) and h₇>0 (h₇ is a real number larger than 0) and h₈>0 (h₈is a real number larger than 0) and h₉>0 (h₉ is a real number largerthan 0) and h₁₀>0 (h₁₀ is a real number larger than 0) and h₁₁>0 (h₁₁ isa real number larger than 0) and h₁₂>0 (h₁₂ is a real number larger than0) and h₁₃>0 (h₁₃ is a real number larger than 0) and h₁₄>0 (h₁₄ is areal number larger than 0),

{h₁≠15 and h₂≠15 and h₃≠15 and h₄≠15 and h₅≠15 and h₆≠15 and h₇≠15,

and h₁≠h₂ and h₁≠h₃ and h₁≠h₄ and h₁≠h₅ and h₁≠h₆ and h₁≠h₇,

and h₂≠h₃ and h₂≠h₄ and h₂≠h₅ and h₂≠h₆ and h₂≠h₇,

and h₃≠h₄ and h₃≠h₅ and h₃≠h₆ and h₃≠h₇,

and h₄≠h₅ and h₄≠h₆ and h₄≠h₇,

and h₅≠h₆ and h₅+h₇,

and h₆+h₇}

and

{h₈≠15 and h₉≠15 and h₁₀≠15 and h₁₁≠15 and h₁₂≠15 and h₁₃≠15 and h₁₄≠15,

and h₈≠h₉ and h₈≠h₁₀ and h₈≠h₁₁ and h₈≠h₁₂ and h₈≠h₁₃ and h₈≠h₁₄,

and h₉≠h₁₀ and h₉≠h₁₁ and h₉≠h₁₂ and h₉≠h₁₃ and h₉≠h₁₄,

and h₁₀≠h₁₁ and h₁₀≠h₁₂ and h₁₀≠h₁₃ and h₁₀≠h₁₄,

and h₁₁≠h₁₂ and h₁₁≠h₁₃ and h₁₁+h₁₄,

and h₁₂≠h₁₃ and h₁₂≠h₁₄,

and h₁₃≠h₁₄}

and

{h₁≠h₈ or h₂≠h₉ or h₃≠h₁₀ or h₄≠h₁₁ or h₅≠h₁₂ or h₆≠h₁₃ or h₇≠h₁₄ holds}hold.”, which necessary point differs from that in the arrangement ofthe signal points of (Supplement 2).

Although the detailed configuration is not illustrated in FIGS. 117 and118 , similarly the modulated signal can be transmitted and receivedusing the OFDM scheme and spectral spread communication scheme, whichare described in another exemplary embodiment.

In the MIMO transmission scheme, the space-time codes such as thespace-time block code (however, the symbol mat be arranged on thefrequency axis), and the MIMO transmission scheme in which the precodingis performed or not performed, which are described in the first totwelfth exemplary embodiments, there is a possibility of improving thedata reception quality even if 16QAM, 64QAM, and 256QAM are used.

(Supplement 4)

The bit length adjusting method is described in the first to eleventhexemplary embodiments. The method for applying the bit length adjustingmethods of the first to eleventh exemplary embodiments to the DVBstandard is described in the twelfth exemplary embodiment. The case that16QAM, 64QAM, and 256QAM are applied as the modulation scheme isdescribed in the above exemplary embodiments. A specific mapping methodwith respect to 16QAM, 64QAM, and 256QAM is described in (Configurationexample R1).

A mapping method with respect to 16QAM, 64QAM, and 256QAM different fromthat of (Configuration example R1), (Supplement 2), and (Supplement 3)will be described below. The following 16QAM, 64QAM, and 256QAM may beapplied to the first to twelfth exemplary embodiments, and the effectsof the first to twelfth exemplary embodiments can also be obtained.

The 16QAM mapping method will be described below. FIG. 119 illustratesan arrangement example of 16QAM signal points in the I-Q plane. In FIG.119 , 16 marks “◯” indicate 16QAM signal points, a horizontal axisindicates I, and a vertical axis indicates Q.

In FIG. 119 , it is assumed that k₁>0 (k₁ is a real number larger than0), k₂>0 (k₂ is a real number larger than 0), k₁≠1, k₂≠1, and k₁≠k₂hold.

In the I-Q plane, 16 signal points included in 16QAM (indicated by themarks “◯” in FIG. 119 ) are obtained as follows. (w_(16c) is a realnumber larger than 0) (k₁×w_(16c),k₂×w_(16c)), (k₁×w_(16c),1×w_(16c)),(k₁×w_(16c),−1×w_(16c)), (k₁×w_(16c),−k₂×w_(16c)),(1×w_(16c),k₂×w_(16c)), (1×w_(16c),1×w_(16c)), (1×w_(16c),−1×w_(16c)),(1×w_(16c),−k₂×w_(16c)), (−1×w_(16c),k₂×w_(16c)), (−1×w_(16c),1×w_(16c)), (−1×w_(16c),−1×w_(16c)), (−1×w_(16c),−k₂×w_(16c)),(−k₁×w_(16c),k₂×w_(16c)), (−k₁×w_(16c), 1×w_(16c)),(−k₁×w_(16c),−1×w_(16c)), (−k₁×w_(16c),−k₂×w_(16c))

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, and b3. For example, for the bits to be transmitted (b0, b1, b2,b3)=(0,0,0,0), the bits are mapped at signal point 11901 in FIG. 119 ,and (I,Q)=(k₁×w_(16c),k₂×w_(16c)) is obtained when I is an in-phasecomponent while Q is a quadrature component of the mapped basebandsignal.

Based on the bits to be transmitted (b0, b1, b2, b3), in-phase componentI and quadrature component Q of the mapped baseband signal are decided(during 16QAM modulation). FIG. 119 illustrates an example of therelationship between the set of b0, b1, b2, and b3 (0000 to 1111) andthe signal point coordinates. Values 0000 to 1111 of the set of b0, b1,b2, and b3 are indicated immediately below 16 signal points included in16QAM (the marks “◯” in FIG. 119 ) (k₁×w_(16c),k₂×w_(16c)),(k₁×w_(16c),1×w_(16c)), (k₁×w_(16c),−1×w_(16c)),(k₁×w_(16c),k₂×w_(16c)), (1×w_(16c),k₂×w_(16c)), (1×w_(16c),1×w_(16c)),(1×w_(16C),−1×w_(16c)), (1×w_(16c),−k₂×w_(16c)),(−1×w_(16c),k₂×w_(16c)), (−1×w_(16C),1×w_(16c)),(−1×w_(16c),−1×w_(16c)), (−1×w_(16c),−k₂×w_(16c)),(−k₁×w_(16c),k₂×w_(16c)), (−k₁×w_(16c),1×w_(16c)),(−k₁×w_(16c),−1×w_(16c)), (−k₁×w_(16c),−k₂×w_(16c)). Respectivecoordinates of the signal points (“◯”) immediately above the values 0000to 1111 of the set of b0, b1, b2, and b3 in the I-Q plane serve asin-phase component I and quadrature component Q of the mapped basebandsignal. The relationship between the set of b0, b1, b2, and b3 (0000 to1111) and the signal point coordinates during 16QAM modulation is notlimited to that in FIG. 119 .

16 signal points in FIG. 119 are named as “signal point 1”, “signalpoint 2”, . . . , “signal point 15”, and “signal point 16” (because ofthe presence of 16 signal points, “signal point 1” to “signal point 16”exist). In the I-Q plane, Di is a distance between “signal point i” andthe origin. At this point, w_(16c) is given by the following equation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 371} \right\rbrack & \; \\\begin{matrix}{w_{16c} = \frac{z}{\sqrt{\frac{\sum\limits_{i = 1}^{16}D_{i}^{2}}{16}}}} \\{= \frac{z}{\sqrt{\frac{\begin{matrix}\left( {{\left( {1^{2} + 1^{2}} \right) \times 4} + {\left( {k_{1}^{2} + k_{2}^{2}} \right) \times 4} +} \right. \\\left. {{\left( {k_{1}^{2} + 1^{2}} \right) \times 4} + {\left( {k_{2}^{2} + 1^{2}} \right) \times 4}} \right)\end{matrix}}{16}}}}\end{matrix} & ({H7})\end{matrix}$

Therefore, the mapped baseband signal has an average power of z₂. Theeffect of 16QAM is described later.

The 64QAM mapping method will be described below. FIG. 120 illustratesan arrangement example of 64QAM signal points in the I-Q plane. In FIG.120 , 64 marks “◯” indicate 64QAM signal points, a horizontal axisindicates I, and a vertical axis indicates Q.

In FIG. 120 , it is assumed that “m₁>0 (m₁ is a real number larger than0) and m₂>0 (m₂ is a real number larger than 0) and m₃>0 (m₃ is a realnumber larger than 0) and m₄>0 (m₄ is a real number larger than 0) andm₅>0 (m₅ is a real number larger than 0) and m₆>0 (m₆ is a real numberlarger than 0) and m₇>0 (m₇ is a real number larger than 0) and m₈>0 (m₈is a real number larger than 0), and

{m₁≠m₂ and m₁≠m₃ and m₁≠m₄ and m₂≠m₃ and m₂≠m₄ and m₃≠m₄}

and

{m₅≠m₆ and m₅≠m₇ and m₅≠m₈ and m₆≠m₇ and m₆≠m₈ and m₇≠m₈}

and

{m₁≠m₅ or m₂≠m₆ or m₃≠m₇ or m₄≠m₈ holds} hold.”

or that

“m₁>0 (m₁ is a real number larger than 0) and m₂>0 (m₂ is a real numberlarger than 0) and m₃>0 (m₃ is a real number larger than 0) and m₄>0 (m₄is a real number larger than 0) and m₅>0 (m₅ is a real number largerthan 0) and m₆>0 (m₆ is a real number larger than 0) and m₇>0 (m₇ is areal number larger than 0) and m₈>0 (m₈ is a real number larger than 0),and{m₁≠m₂ and m₁≠m₃ and m₁≠m₄ and m₂≠m₃ and m₂≠m₄ and m₃≠m₄}and{m₅≠m₆ and m₅≠m₇ and m₅+m₈ and m₆≠m₇ and m₆≠m₈ and m₇≠m₈}and{m₁≠m₅ or m₂≠m₆ or m₃≠m₇ or m₄+m₈ holds}and{m₁=m₅ or m₂=m₆ or m₃=m₇ or m₄=m₈ holds} hold.”

In the I-Q plane, 64 signal points included in 64QAM (indicated by themarks “◯” in FIG. 120 ) are obtained as follows. (w_(64c) is a realnumber larger than 0)

(m₄×w_(64c),m₈×w_(64c)), (m₄×w_(64c),m₇×w_(64c)),(m₄×w_(64c),m₆×w_(64c)), (m₄×w_(64c),m₅×w_(64c)),(m₄×w_(64c),−m₅×w_(64c)), (m₄×w_(64c),−m₆×w_(64c)),(m₄×w_(64c),−m₇×w_(64c)), (m₄×w_(64c),−m₈×w_(64c))

(m₃×w_(64c), m₈×w_(64c)), (m₃×w_(64c),m₇×w_(64c)), (m₃×w_(64c),m₆×w_(64c)), (m₃×w_(64c), m₅×w_(64c)), (m₃×w_(64c),−m₅×w_(64c)),(m₃×w_(64c),−m₆×w_(64c)), (m₃×w_(64c),−m₇×w_(64c)),(m₃×w_(64c),−m₈×w_(64c))

(m₂×w_(64c), m₈×w_(64c)), (m₂×w_(64c), m₇×w_(64c)), (m₂×w_(64c),m₆×w_(64c)), (m₂×w_(64c), m₅×w_(64c)), (m₂×w_(64c),−m₅×w_(64c)),(m₂×w_(64c),−m₆×w_(64c)), (m₂×w_(64c),−m₇×w_(64c)),(m₂×w_(64c),−m₈×w_(64c))

(m₁×w_(64c),m₈×w_(64c)), (m₁×w_(64c),m₇×w_(64c)),(m₁×w_(64c),m₆×w_(64c)), (m₁×w_(64c),m₅×w_(64c)),(m₁×w_(64c),−m₅×w_(64c)), (m₁×w_(64c),−m₆×w_(64c)),(m₁×w_(64c),−m₇×w_(64c)), (m₁×w_(64c),−m₈×w_(64c))

(−m₁×w_(64c),m₈×w_(64c)), (−m₁×w_(64c),m₇×w_(64c)),(−m₁×w_(64c),m₆×w_(64c)), (−m₁×w_(64c),m₅×w_(64c)),(−m₁×w_(64c),−m₅×w_(64c)), (−m₁×w_(64c),−m₆×w_(64c)),(−m₁×w_(64c),−m₇×w_(64c)), (−m₁×w_(64c),−m₈×w_(64c))

(−m₂×w_(64c),m₈×w_(64c)), (−m₂×w_(64c),m₇×w_(64c)),(−m₂×w_(64c),m₆×w_(64c)), (−m₂×w_(64c), m₅×w_(64c)),(−m₂×w_(64c),−m₅×w_(64c)), (−m₂×w_(64c),−m₆×w_(64c)),(−m₂×w_(64c),−m₇×w_(64c)), (−m₂×w_(64c),−m₈×w_(64c))

(−m₃×w_(64c),m₈×w_(64c)), (−m₃×w_(64c), m₇×w_(64c)), (−m₃×w_(64c),m₆×w_(64c)), (−m₃×w_(64c), m₅×w_(64c)), (−m₃×w_(64c),−m₅×w_(64c)),(−m₃×w_(64c),−m₆×w_(64c)), (−m₃×w_(64c),−m₇×w_(64c)),(−m₃×w_(64c),−m₈×w_(64c))

(−m₄×w_(64c),m₈×w_(64c)), (−m₄×w_(64c),m₇×w_(64c)),(−m₄×w_(64c),m₆×w_(64c)), (−m₄×w_(64c),m₅×w_(64c)),(−m₄×w_(64c),−m₅×w_(64c)), (−m₄×w_(64c),−m₆×w_(64c)),(−m₄×w_(64c),−m₇×w_(64c)), (−m₄×w_(64c),−m₈×w_(64c))

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, and b5. For example, for the bits to be transmitted (b0,b1, b2, b3, b4, b5)=(0,0,0,0,0,0), the bits are mapped at signal point12001 in FIG. 120 , and (I,Q)=(m₄×w_(64c),m₈×w_(64c)) is obtained when Iis an in-phase component while Q is a quadrature component of the mappedbaseband signal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5), in-phasecomponent I and quadrature component Q of the mapped baseband signal aredecided (during 64QAM modulation). FIG. 120 illustrates an example of arelationship between the set of b0, b1, b2, b3, b4, and b5 (000000 to111111) and the signal point coordinates. Values 000000 to 111111 of theset of b0, b1, b2, b3, b4, and b5 are indicated immediately below 64signal points included in 64QAM (the marks “◯” in FIG. 120 )(m₄×w_(64c),m₈×w_(64c)), (m₄×w_(64c),m₇×w_(64c)),(m₄×w_(64c),m₆×w_(64c)), (m₄×w_(64c),m₅×w_(64c)),(m₄×w_(64c),−m₅×w_(64c)), (m₄×w_(64c),−m₆×w_(64c)),(m₄×w_(64c),−m₇×w_(64c)), (m₄×w_(64c),−m₈×w_(64c))

(m₃×w_(64c), m₈×w_(64c)), (m₃×w_(64c), m₇×w_(64c)), (m₃×w_(64c),m₆×w_(64c)), (m₃×w_(64c), m₅×w_(64c)), (m₃×w_(64c),−m₅×w_(64c)),(m₃×w_(64c),−m₆×w_(64c)), (m₃×w_(64c),−m₇×w_(64c)),(m₃×w_(64c),−m₈×w_(64c))

(m₂×w_(64c), m₈×w_(64c)), (m₂×w_(64c),m₇×w_(64c)), (m₂×w_(64c),m₆×w_(64c)), (m₂×w_(64c), m₅×w_(64c)), (m₂×w_(64c),−m₅×w_(64c)),(m₂×w_(64c),−m₆×w_(64c)), (m₂×w_(64c),−m₇×w_(64c)),(m₂×w_(64c),−m₈×w_(64c))

(m₁×w_(64c),m₈×w_(64c)), (m₁×w_(64c),m₇×w_(64c)),(m₁×w_(64c),m₆×w_(64c)), (m₁×w_(64c),m₅×w_(64c)),(m₁×w_(64c),−m₅×w_(64c)), (m₁×w_(64c),−m₆×w_(64c)),(m₁×w_(64c),−m₇×w_(64c)), (m₁×w_(64c),−m₈×w_(64c))

(−m₁×w_(64c),m₈×w_(64c)), (−m₁×w_(64c),m₇×w_(64c)),(−m₁×w_(64c),m₆×w_(64c)), (−m₁×w_(64c),m₅×w_(64c)),(−m₁×w_(64c),−m₅×w_(64c)), (−m₁×w_(64c),−m₆×w_(64c)),(−m₁×w_(64c),−m₇×w_(64c)), (−m₁×w_(64c),−m₈×w_(64c))

(−m₂×w_(64c), m₈×w_(64c)), (−m₂×w_(64c),m₇×w_(64c)), (−m₂×w_(64c),m₆×w_(64c)), (−m₂×w_(64c), m₅×w_(64c)), (−m₂×w_(64c),−m₅×w_(64c)),(−m₂×w_(64c),−m₆×w_(64c)), (−m₂×w_(64c),−m₇×w_(64c)),(−m₂×w_(64c),−m₈×w_(64c))

(−m₃×w_(64c),m₈×w_(64c)), (−m₃×w_(64c), m₇×w_(64c)),(−m₃×w_(64c),m₆×w_(64c)), (−m₃×w_(64c),m₅×w_(64c)),(−m₃×w_(64c),−m₅×w_(64c)), (−m₃×w_(64c),−m₆×w_(64c)),(−m₃×w_(64c),−m₇×w_(64c)), (−m₃×w_(64c),−m₈×w_(64c))

(−m₄×w_(64c),m₈×w_(64c)), (−m₄×w_(64c),m₇×w_(64c)),(−m₄×w_(64c),m₆×w_(64c)), (−m₄×w_(64c),m₅×w_(64c)),(−m₄×w_(64c),−m₅×w_(64c)), (−m₄×w_(64c),−m₆×w_(64c)),(−m₄×w_(64c),−m₇×w_(64c)), (−m₄×w_(64c),−m₈×w_(64c)). Respectivecoordinates of the signal points (“◯”) immediately above the values000000 to 111111 of the set of b0, b1, b2, b3, b4, and b5 in the I-Qplane serve as in-phase component I and quadrature component Q of themapped baseband signal. The relationship between the set of b0, b1, b2,b3, b4, and b5 (000000 to 111111) and the signal point coordinatesduring 64QAM modulation is not limited to that in FIG. 120 .

64 signal points in FIG. 120 are named as “signal point 1”, “signalpoint 2”, . . . , “signal point 63”, and “signal point 64” (because ofthe presence of 64 signal points, “signal point 1” to “signal point 64”exist). In the I-Q plane, Di is a distance between “signal point i” andthe origin. At this point, w_(64c) is given by the following equation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 372} \right\rbrack & \; \\{w_{64c} = \frac{z}{\sqrt{\frac{\sum\limits_{i = 1}^{64}D_{i}^{2}}{64}}}} & ({H8})\end{matrix}$

Therefore, the mapped baseband signal has an average power of z₂. Theeffect is described later.

The 256QAM mapping method will be described below. FIG. 121 illustratesan arrangement example of 256QAM signal points in the I-Q plane. In FIG.121 , 256 marks “◯” indicate 256QAM signal points, a horizontal axisindicates I, and a vertical axis indicates Q.

In FIG. 121 , it is assumed that “n₁>0 (n₁ is a real number larger than0) and n₂>0 (n₂ is a real number larger than 0) and n₃>0 (m is a realnumber larger than 0) and n₄>0 (n₄ is a real number larger than 0) andn₅>0 (n₆ is a real number larger than 0) and n₇>0 (n₇ is a real numberlarger than 0) and n₈>0 (n₈ is a real number larger than 0)

and n₉>0 (n₉ is a real number larger than 0) and n₁₀>0 (n₁₀ is a realnumber larger than 0) and n₁₁>0 (n₁₁ is a real number larger than 0) andn₁₂>0 (n₁₂ is a real number larger than 0) and n₁₃>0 (n₁₃ is a realnumber larger than 0) and n₁₄>0 (n₁₄ is a real number larger than 0) andn₁₅>0 (n₁₅ is a real number larger than 0) and n₁6>0 (n₁₆ is a realnumber larger than 0), and{n₁≠n₂ and n₁≠n₃ and n₁≠n₄ and n₁≠n₅ and n₁≠n₆ and n₁≠n₇ and n₁≠n₈and n₂≠n₃ and n₂≠n₄ and n₂≠n₅ and n₂≠n₆ and n₂≠n₇ and n₂≠n₈and n₃≠n₄ and n₃≠n₅ and n₃≠n₆ and n₃≠n₇ and n₃≠n₈and n₄≠n₅ and n₄≠n₆ and n₄≠n₇ and n₄≠n₅and n₅≠n₆ and n₅≠n₇ and n₅≠n₈and n₆≠n₇ and n₆≠n₈and n₇≠n₈}and{n₉≠n₁₀ and n₉≠n₁₁ and n₉≠n₁₂ and n₉≠n₁₃ and n₉≠n₁₄ and n₉≠n₁₅ andn₉≠n₁₆and n₁₀≠n₁₁ and n₁₀≠n₁₂ and n₁₀≠n₁₃ and n₁₀≠n₁₄ and n₁₀≠n₁₅ and n₁₀≠n₁₆and n₁₁≠n₁₂ and n₁₁≠n₁₃ and n₁₁≠n₁₄ and n₁₁≠n₁₅ and n₁₁≠n₁₆and n₁₂≠n₁₃ and n₁₂≠n₁₄ and n₁₂≠n₁₅ and n₁₂≠n₁₆and n₁₃≠n₁₄ and n₁₃≠n₁₅ and n₁₃≠n₁₆and n₁₄≠n₁₅ and n₁₄≠n₁₆and n₁₅≠n₁₆}and{n₁≠n₉ or n₂≠n₁₀ or n₃≠n₁₁ or n₄≠n₁₂ or n₅≠n₁₃ or n₆≠n₁₄ or n₇≠n₁₅ orn₈≠n₁₆ holds} hold”.orthat “n₁>0 (n₁ is a real number larger than 0) and n₂>0 (n₂ is a realnumber larger than 0)and n₃>0 (n₃ is a real number larger than 0) and n₄>0 (n₄ is a realnumber larger than 0)and n₅>0 (n₆ is a real number larger than 0) and n₇>0 (n₇ is a realnumber larger than 0)and n₈>0 (n₈ is a real number larger than 0)and n₉>0 (n₉ is a real number larger than 0) and n₁₀>0 (n₁₀ is a realnumber larger than 0)and n₁₁>0 (n₁₁ is a real number larger than 0) and n₁₂>0 (n₁₂ is a realnumber larger than 0) and n₁₃>0 (n₁₃ is a real number larger than 0) andn₁₄>0 (n₁₄ is a real number larger than 0) and n₁₅>0 (n₁₅ is a realnumber larger than 0) and n₁₆>0 (n₁₆ is a real number larger than 0),and{n₁≠n₂ and n₁≠n₃ and n₁≠n₄ and n₁≠n₅ and n₁≠n₆ and n₁≠n₇ and n₁≠n₈and n₂≠n₃ and n₂≠n₄ and n₂≠n₅ and n₂≠n₆ and n₂≠n₇ and n₂≠n₈and n₃≠n₄ and n₃≠n₅ and n₃≠n₆ and n₃≠n₇ and n₃≠n₈and n₄≠n₅ and n₄≠n₆ and n₄≠n₇ and n₄≠n₈and n₅≠n₆ and n₅≠n₇ and n₅≠n₈and n₆≠n₇ and n₆≠n₈and n₇≠n₈}and{n₉≠n₁₀ and n₉≠n₁₁ and n₉≠n₁₂ and n₉≠n₁₃ and n₉≠n₁₄ and n₉≠n₁₅ andn₉≠n₁₆and n₁₀≠n₁₁ and n₁₀≠n₁₂ and n₁₀≠n₁₃ and n₁₀≠n₁₄ and n₁₀≠n₁₅ and n₁₀+n₁₆and n₁₁≠n₁₂ and n₁₁≠n₁₃ and n₁₁≠n₁₄ and n₁₁≠n₁₅ and n₁₁≠n₁₆and n₁₂≠n₁₃ and n₁₂≠n₁₄ and n₁₂≠n₁₅ and n₁₂≠n₁₆and n₁₃≠n₁₄ and n₁₃≠n₁₅ and n₁₃≠n₁₆and n₁₄≠n₁₅ and n₁₄≠n₁₆and n₁₅≠n₁₆}and{n₁≠n₉ or n₂≠n₁₀ or n₃≠n₁₁ or n₄≠n₁₂ or n₅≠n₁₃ or n₆≠n₁₄ or n₇≠n₁₅ orn₈≠n₁₆ holds}and{n₁=n₉ or n₂=n₁₀ or n₃=n₁₁ or n₄=n₁₂ or n₅=n₁₃ or n₆=n₁₄ or n₇=n₁₅ orn₈=n₁₆ holds} hold.”

In the I-Q plane, 256 signal points included in 256QAM (indicated by themarks “◯” in FIG. 121 ) are obtained as follows. (w_(256c) is a realnumber larger than 0) (n₈×w_(256c),n₁₆×w_(256c)),(n₈×w_(256c),n₁₅×w_(256c)), (n₈×w_(256c), n₁₄×w_(256c)),(n₈×w_(256c),n₁₃×w_(256c)), (n₈×w_(256c),n₁₂×w_(256c)),(n₈×w_(256c),n₁₁×w_(256c)), (n₈×w_(256c),n₁₀×w_(256c)),(n₈×w_(256c),n₉×w_(256c)),

(n₈×w_(256c),−n₁₆×w_(256c)), (n₈×w_(256c),−n₁₅×w_(256c)),(n₈×w_(256c),−n₁₄×w_(256c)), (n₈×w_(256c),−n₁₃×w_(256c)),(n₈×w_(256c),−n₁₂×w_(256c)), (n₈×w_(256c),−n₁₁×w_(256c)),(n₈×w_(256c),−n₁₀×w_(256c)), (n₈×w_(256c),−n₉×w_(256c)),

(n₇×w_(256c), n₁₆×w_(256c)), (n₇×w_(256c),n₁₅×w_(256c)), (n₇×w_(256c),n₁₄×w_(256c)), (n₇×w_(256c),n₁₃×w_(256c)), (n₇×w_(256c),n₁₂×w_(256c)),(n₇×w_(256c),n₁₁×w_(256c)), (n₇×w_(256c),n₁₀×w_(256c)),(n₇×w_(256c),n₉×w_(256c)), (n₇×w_(256c),−n₁₆×w_(256c)),(n₇×w_(256c),−n₁₅×w_(256c)), (n₇×w_(256c),−n₁₄×w_(256c)),(n₇×w_(256c),−n₁₃×w_(256c)), (n₇×w_(256c),−n₁₂×w_(256c)),(n₇×w_(256c),−n₁₁×w_(256c)), (n₇×w_(256c),−n₁₀×w_(256c)),(n₇×w_(256c),−n₉×w_(256c)),(n₆×w_(256c),n₁₆×w_(256c)), (n₆×w_(256c),n₁₅×w_(256c)), (n₆×w_(256c),n₁₄×w_(256c)), (n₆×w_(256c),n₁₃×w_(256c)), (n₆×w_(256c),n₁₂×w_(256c)),(n₆×w_(256c),n₁₁×w_(256c)), (n₆×w_(256c),n₁₀×w_(256c)),(n₆×w_(256c),n₉×w_(256c)), (n₆×w_(256c),−n₁₆×w_(256c)),(n₆×w_(256c),−n₁₅×w_(256c)), (n₆×w_(256c),−n₁₄×w_(256c)),(n₆×w_(256c),−n₁₃×w_(256c)), (n₆×w_(256c),−n₁₂×w_(256c)),(n₆×w_(256c),−n₁₁×w_(256c)), (n₆×w_(256c),−n₁₀×w_(256c)),(n₆×w_(256c),−n₉×w_(256c)),(n₅×w_(256c),n₁₆×w_(256c)), (n₅×w_(256c),n₁₅×w_(256c)), (n₅×w_(256c),n₁₄×w_(256c)), (n₅×w_(256c),n₁₃×w_(256c)), (n₅×w_(256c),n₁₂×w_(256c)),(n₅×w_(256c),n₁₁×w_(256c)), (n₅×w_(256c),n₁₀×w_(256c)),(n₅×w_(256c),n₉×w_(256c)), (n₅×w_(256c),−n₁₆×w_(256c)),(n₅×w_(256c),−n₁₅×w_(256c)), (n₅×w_(256c),−n₁₄×w_(256c)),(n₅×w_(256c),−n₁₃×w_(256c)), (n₅×w_(256c),−n₁₂×w_(256c)),(n₅×w_(256c),−n₁₁×w_(256c)), (n₅×w_(256c),−n₁₀×w_(256c)),(n₅×w_(256c),−n₉×w_(256c)),(n₄×w_(256c), n₁₆×w_(256c)), (n₄×w_(256c),n₁₅×w_(256c)), (n₄×w_(256c),n₁₄×w_(256c)), (n₄×w_(256c),n₁₃×w_(256c)), (n₄×w_(256c), n₁₂×w_(256c)),(n₄×w_(256c), n₁₁×w_(256c)), (n₄×w_(256c),n₁₀×w_(256c)), (n₄×w_(256c),n₉×w_(256c)), (n₄×w_(256c),−n₁₆×w_(256c)), (n₄×w_(256c),−n₁₅×w_(256c)),(n₄×w_(256c),−n₁₄×w_(256c)), (n₄×w_(256c),−n₁₃×w_(256c)),(n₄×w_(256c),−n₁₂×w_(256c)), (n₄×w_(256c),−n₁₁×w_(256c)),(n₄×w_(256c),−n₁₀×w_(256c)), (n₄×w_(256c),−n₉×w_(256c)),(n₃×w_(256c), n₁₆×w_(256c)), (n₃×w_(256c),n₁₅×w_(256c)), (n₃×w_(256c),n₁₄×w_(256c)), (n₃×w_(256c),n₁₃×w_(256c)), (n₃×w_(256c),n₁₂×w_(256c)),(n₃×w_(256c),n₁₁×w_(256c)), (n₃×w_(256c),n₁₀×w_(256c)),(n₃×w_(256c),n₉×w_(256c)), (n₃×w_(256c),−n₁₆×w_(256c)),(n₃×w_(256c),−n₁₅×w_(256c)), (n₃×w_(256c),−n₁₄×w_(256c)),(n₃×w_(256c),−n₁₃×w_(256c)), (n₃×w_(256c),−n₁₂×w_(256c)),(n₃×w_(256c),−n₁₁×w_(256c)), (n₃×w_(256c),−n₁₀×w_(256c)),(n₃×w_(256c),−n₉×w_(256c)),(n₂×w_(256c), n₁₆×w_(256c)), (n₂×w_(256c),n₁₅×w_(256c)), (n₂×w_(256c),n₁₄×w_(256c)), (n₂×w_(256c),n₁₃×w_(256c)), (n₂×w_(256c), n₁₂×w_(256c)),(n₂×w_(256c), n₁₁×w_(256c)), (n₂×w_(256c),n₁₀×w_(256c)), (n₂×w_(256c),n₉×w_(256c)), (n₂×w_(256c),−n₁₆×w_(256c)), (n₂×w_(256c),−n₁₅×w_(256c)),(n₂×w_(256c),−n₁₄×w_(256c)), (n₂×w_(256c),−n₁₃×w_(256c)),(n₂×w_(256c),−n₁₂×w_(256c)), (n₂×w_(256c),−n₁₁×w_(256c)),(n₂×w_(256c),−n₁₀×w_(256c)), (n₂×w_(256c),−n₉×w_(256c)),(n₁×w_(256c),n₁₆×w_(256c)), (n₁×w_(256c),n₁₅×w_(256c)),(n₁×w_(256c),n₁₄×w_(256c)), (n₁×w_(256c),n₁₃×w_(256c)),(n₁×w_(256c),n₁₂×w_(256c)), (n₁×w_(256c),n₁₁×w_(256c)),(n₁×w_(256c),n₁₀×w_(256c)), (n₁×w_(256c), n₉×w_(256c)),(n₁×w_(256c),−n₁₆×w_(256c)), (n₁×w_(256c),−n₁₅×w_(256c)),(n₁×w_(256c),−n₁₄×w_(256c)), (n₁×w_(256c),−n₁₃×w_(256c)),(n₁×w_(256c),−n₁₂×w_(256c)), (n₁×w_(256c),−n₁₁×w_(256c)),(n₁×w_(256c),−n₁₀×w_(256c)), (n₁×w_(256c),−n₉×w_(256c)),(−n₈×w_(256c),n₁₆×w_(256c)), (−n₈×w_(256c),n₁₅×w_(256c)), (−n₈×w_(256c),n₁₄×w_(256c)), (−n₈×w_(256c),n₁₃×w_(256c)), (−n₈×w_(256c),n₁₂×w_(256c)),(−n₈×w_(256c),n₁₁×w_(256c)), (−n₈×w_(256c),n₁₀×w_(256c)),(−n₈×w_(256c),n₉×w_(256c)), (−n₈×w_(256c),−n₁₆×w_(256c)),(−n₈×w_(256c),n₁₅×w_(256c)), (−n₈×w_(256c),−n₁₄×w_(256c)),(−n₈×w_(256c),−n₁₃×w_(256c)), (−n₈×w_(256c),−n₁₂×w_(256c)),(−n₈×w_(256c),−n₁₁×w_(256c)), (−n₈×w_(256c), −n₁₀×w_(256c)),(−n₈×w_(256c), −n₉×w_(256c)),(−n₇×w_(256c), n₁₆×w_(256c)), (−n₇×w_(256c),n₁₅×w_(256c)),(−n₇×w_(256c), n₁₄×w_(256c)), (−n₇×w_(256c),n₁₃×w_(256c)),(−n₇×w_(256c),n₁₂×w_(256c)), (−n₇×w_(256c),n₁₁×w_(256c)),(−n₇×w_(256c),n₁₀×w_(256c)), (−n₇×w_(256c),n₉×w_(256c)),(−n₇×w_(256c),−n₁₆×w_(256c)), (−n₇×w_(256c),−n₁₅×w_(256c)),(−n₇×w_(256c),−n₁₄×w_(256c)), (−n₇×w_(256c),−n₁₃×w_(256c)),(−n₇×w_(256c),−n₁₂×w_(256c)), (−n₇×w_(256c),−n₁₁×w_(256c)),(−n₇×w_(256c), −n₁₀×w_(256c)), (−n₇×w_(256c), n₉×w_(256c)),(−n₆×w_(256c),n₁₆×w_(256c)), (−n₆×w_(256c),n₁₅×w_(256c)), (−n₆×w_(256c),n₁₄×w_(256c)), (−n₆×w_(256c),n₁₃×w_(256c)), (−n₆×w_(256c),n₁₂×w_(256c)), (−n₆×w_(256c), n₁₁×w_(256c)), (−n₆×w_(256c),n₁₀×w_(256c)), (−n₆×w_(256c), n₉×w_(256c)),(−n₆×w_(256c),−n₁₆×w_(256c)), (−n₆×w_(256c),−n₁₅×w_(256c)),(−n₆×w_(256c),−n₁₄×w_(256c)), (−n₆×w_(256c),−n₁₃×w_(256c)),(−n₆×w_(256c),−n₁₂×w_(256c)), (−n₆×w_(256c),−n₁₁×w_(256c)),(−n₆×w_(256c),−n₁₀×w_(256c)), (−n₆×w_(256c),−n₉×w_(256c)),(−n₅×w_(256c),n₁₆×w_(256c)), (−n₅×w_(256c),n₁₅×w_(256c)), (−n₅×w_(256c),n₁₄×w_(256c)), (−n₅×w_(256c),n₁₃×w_(256c)), (−n₅×w_(256c),n₁₂×w_(256c)),(−n₅×w_(256c), n₁₁×w_(256c)), (−n₅×w_(256c), n₁₀×w_(256c)),(−n₅×w_(256c), n₉×w_(256c)), (−n₅×w_(256c),−n₁₆×w_(256c)),(−n₅×w_(256c),−n₁₅×w_(256c)), (−n₅×w_(256c),−n₁₄×w_(256c)),(−n₅×w_(256c),−n₁₃×w_(256c)), (−n₅×w_(256c),−n₁₂×w_(256c)),(−n₅×w_(256c),−n₁₁×w_(256c)), (−n₅×w_(256c), −n₁₀×w_(256c)),(−n₅×w_(256c), −n₉×w_(256c)),(−n₄×w_(256c), n₁₆×w_(256c)), (−n₄×w_(256c),n₁₅×w_(256c)),(−n₄×w_(256c), n₁₄×w_(256c)), (−n₄×w_(256c),n₁₃×w_(256c)),(−n₄×w_(256c),n₁₂×w_(256c)), (−n₄×w_(256c),n₁₁×w_(256c)),(−n₄×w_(256c),n₁₀×w_(256c)), (−n₄×w_(256c),n₉×w_(256c)),(−n₄×w_(256c),−n₁₆×w_(256c)), (−n₄×w_(256c),−n₁₅×w_(256c)),(−n₄×w_(256c),−n₁₄×w_(256c)), (−n₄×w_(256c),−n₁₃×w_(256c)),(−n₄×w_(256c),−n₁₂×w_(256c)), (−n₄×w_(256c),−n₁₁×w_(256c)),(−n₄×w_(256c),−n₁₀×w_(256c)), (−n₄×w_(256c), −n₉×w_(256c)),(−n₃×w_(256c), n₁₆×w_(256c)), (−n₃×w_(256c),n₁₅×w_(256c)),(−n₃×w_(256c), n₁₄×w_(256c)), (−n₃×w_(256c),n₁₃×w_(256c)),(−n₃×w_(256c), n₁₂×w_(256c)), (−n₃×w_(256c), n₁₁×w_(256c)),(−n₃×w_(256c), n₁₀×w_(256c)), (−n₃×w_(256c), n₉×w_(256c)),(−n₃×w_(256c),−n₁₆×w_(256c)), (−n₃×w_(256c),−n₁₅×w_(256c)),(−n₃×w_(256c),−n₁₄×w_(256c)), (−n₃×w_(256c),−n₁₃×w_(256c)),(−n₃×w_(256c),−n₁₂×w_(256c)), (−n₃×w_(256c),−n₁₁×w_(256c)),(−n₃×w_(256c), −n₁₀×w_(256c)), (−n₃×w_(256c), n₉×w_(256c)),(−n₂×w_(256c), n₁₆×w_(256c)), (−n₂×w_(256c),n₁₅×w_(256c)),(−n₂×w_(256c), n₁₄×w_(256c)), (−n₂×w_(256c),n₁₃×w_(256c)),(−n₂×w_(256c),n₁₂×w_(256c)), (−n₂×w_(256c),n₁₁×w_(256c)),(−n₂×w_(256c),n₁₀×w_(256c)), (−n₂×w_(256c),n₉×w_(256c)),(−n₂×w_(256c),−n₁₆×w_(256c)), (−n₂×w_(256c),−n₁₅×w_(256c)),(−n₂×w_(256c),−n₁₄×w_(256c)), (−n₂×w_(256c),−n₁₃×w_(256c)),(−n₂×w_(256c),−n₁₂×w_(256c)), (−n₂×w_(256c),−n₁₁×w_(256c)),(−n₂×w_(256c), −n₁₀×w_(256c)), (−n₂×w_(256c), n₉×w_(256c)),(−n₁×w_(256c),n₁₆×w_(256c)), (−n₁×w_(256c),n₁₅×w_(256c)),(−n₁×w_(256c),n₁₄×w_(256c)), (−n₁×w_(256c),n₁₃×w_(256c)),(−n₁×w_(256c),n₁₂×w_(256c)), (−n₁×w_(256c), n₁₁×w_(256c)),(−n₁×w_(256c),n₁₀×w_(256c)), (−n₁×w_(256c), n₉×w_(256c)),(−n₁×w_(256c),−n₁₆×w_(256c)), (−n₁×w_(256c),−n₁₅×w_(256c)),(−n₁×w_(256c),−n₁₄×w_(256c)), (−n₁×w_(256c),−n₁₃×w_(256c)),(−n₁×w_(256c),−n₁₂×w_(256c)), (−n₁×w_(256c),−n₁₁×w_(256c)),(−n₁×w_(256c),−n₁₀×w_(256c)), (−n₁×w_(256c),−n₉×w_(256c))

At this point, the bits to be transmitted (input bits) are set to b0,b1, b2, b3, b4, b5, b6, and b7. For example, for the bits to betransmitted (b0, b1, b2, b3, b4, b5, b6, b7)=(0,0,0,0,0,0,0,0), the bitsare mapped at signal point 12101 in FIG. 121 , and(I,Q)=(n₈×w_(256c),n₁₆×w_(256c)) is obtained when I is an in-phasecomponent while Q is a quadrature component of the mapped basebandsignal.

Based on the bits to be transmitted (b0, b1, b2, b3, b4, b5, b6, b7),in-phase component I and quadrature component Q of the mapped basebandsignal are decided (during 256QAM modulation). FIG. 121 illustrates anexample of a relationship between the set of b0, b1, b2, b3, b4, b5, b6,and b7 (00000000 to 11111111) and the signal point coordinates. Values00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6, and b7are indicated immediately below 256 signal points included in 256QAM(the marks “◯” in FIG. 121 ) (n₈×w_(256c),n₁₆×w_(256c)),(n₈×w_(256c),n₁₅×w_(256c)), (n₈×w_(256c), n₁₄×w_(256c)),(n₈×w_(256c),n₁₃×w_(256c)), (n₈×w_(256c),n₁₂×w_(256c)),(n₈×w_(256c),n₁₁×w_(256c)), (n₈×w_(256c),n₁₀×w_(256c)), (n₈×w_(256c),n₉×w_(256c)),

(n₈×w_(256c),−n₁₆×w_(256c)), (n₈×w_(256c),−n₁₅×w_(256c)),(n₈×w_(256c),−n₁₄×w_(256c)), (n₈×w_(256c),−n₁₃×w_(256c)),(n₈×w_(256c),−n₁₂×w_(256c)), (n₈×w_(256c),−n₁₁×w_(256c)),(n₈×w_(256c),−n₁₀×w_(256c)), (n₈×w_(256c),−n₉×w_(256c)),

(n₇×w_(256c), n₁₆×w_(256c)), (n₇×w_(256c),n₁₅×w_(256c)), (n₇×w_(256c),n₁₄×w_(256c)), (n₇×w_(256c),n₁₃×w_(256c)), (n₇×w_(256c),n₁₂×w_(256c)),(n₇×w_(256c),n₁₁×w_(256c)), (n₇×w_(256c),n₁₀×w_(256c)),(n₇×w_(256c),n₉×w_(256c)), (n₇×w_(256c),−n₁₆×w_(256c)),(n₇×w_(256c),−n₁₅×w_(256c)), (n₇×w_(256c),−n₁₄×w_(256c)),(n₇×w_(256c),−n₁₃×w_(256c)), (n₇×w_(256c),−n₁₂×w_(256c)),(n₇×w_(256c),−n₁₁×w_(256c)), (n₇×w_(256c),−n₁₀×w_(256c)),(n₇×w_(256c),−n₉×w_(256c)),(n₆×w_(256c), n₁₆×w_(256c)), (n₆×w_(256c),n₁₅×w_(256c)), (n₆×w_(256c),n₁₄×w_(256c)), (n₆×w_(256c),n₁₃×w_(256c)), (n₆×w_(256c),n₁₂×w_(256c)),(n₆×w_(256c),n₁₁×w_(256c)), (n₆×w_(256c),n₁₀×w_(256c)),(n₆×w_(256c),n₉×w_(256c)), (n₆×w_(256c),−n₁₆×w_(256c)),(n₆×w_(256c),−n₁₅×w_(256c)), (n₆×w_(256c),−n₁₄×w_(256c)),(n₆×w_(256c),−n₁₃×w_(256c)), (n₆×w_(256c),−n₁₂×w_(256c)),(n₆×w_(256c),−n₁₁×w_(256c)), (n₆×w_(256c),−n₁₀×w_(256c)),(n₆×w_(256c),−n₉×w_(256c)),(n₅×w_(256c), n₁₆×w_(256c)), (n₅×w_(256c),n₁₅×w_(256c)), (n₅×w_(256c),n₁₄×w_(256c)), (n₅×w_(256c),n₁₃×w_(256c)), (n₅×w_(256c),n₁₂×w_(256c)),(n₅×w_(256c),n₁₁×w_(256c)), (n₅×w_(256c),n₁₀×w_(256c)),(n₅×w_(256c),n₉×w_(256c)), (n₅×w_(256c),−n₁₆×w_(256c)),(n₅×w_(256c),−n₁₅×w_(256c)), (n₅×w_(256c),−n₁₄×w_(256c)),(n₅×w_(256c),−n₁₃×w_(256c)), (n₅×w_(256c),−n₁₂×w_(256c)),(n₅×w_(256c),−n₁₁×w_(256c)), (n₅×w_(256c),−n₁₀×w_(256c)),(n₅×w_(256c),−n₉×w_(256c)),(n₄×w_(256c), n₁₆×w_(256c)), (n₄×w_(256c),n₁₅×w_(256c)), (n₄×w_(256c),n₁₄×w_(256c)), (n₄×w_(256c),n₁₃×w_(256c)), (n₄×w_(256c), n₁₂×w_(256c)),(n₄×w_(256c), n₁₁×w_(256c)), (n₄×w_(256c),n₁₀×w_(256c)), (n₄×w_(256c),n₉×w_(256c)), (n₄×w_(256c),−n₁₆×w_(256c)), (n₄×w_(256c),−n₁₅×w_(256c)),(n₄×w_(256c),−n₁₄×w_(256c)), (n₄×w_(256c),−n₁₃×w_(256c)),(n₄×w_(256c),−n₁₂×w_(256c)), (n₄×w_(256c),−n₁₁×w_(256c)),(n₄×w_(256c),−n₁₀×w_(256c)), (n₄×w_(256c),−n₉×w_(256c)),(n₃×w_(256c), n₁₆×w_(256c)), (n₃×w_(256c),n₁₅×w_(256c)), (n₃×w_(256c),n₁₄×w_(256c)), (n₃×w_(256c),n₁₃×w_(256c)), (n₃×w_(256c),n₁₂×w_(256c)),(n₃×w_(256c),n₁₁×w_(256c)), (n₃×w_(256c),n₁₀×w_(256c)),(n₃×w_(256c),n₉×w_(256c)), (n₃×w_(256c),−n₁₆×w_(256c)),(n₃×w_(256c),−n₁₅×w_(256c)), (n₃×w_(256c),−n₁₄×w_(256c)),(n₃×w_(256c),−n₁₃×w_(256c)), (n₃×w_(256c),−n₁₂×w_(256c)),(n₃×w_(256c),−n₁₁×w_(256c)), (n₃×w_(256c),−n₁₀×w_(256c)),(n₃×w_(256c),−n₉×w_(256c)),(n₂×w_(256c), n₁₆×w_(256c)), (n₂×w_(256c),n₁₅×w_(256c)), (n₂×w_(256c),n₁₄×w_(256c)), (n₂×w_(256c),n₁₃×w_(256c)), (n₂×w_(256c),n₁₂×w_(256c)),(n₂×w_(256c),n₁₁×w_(256c)), (n₂×w_(256c),n₁₀×w_(256c)),(n₂×w_(256c),n₉×w_(256c)), (n₂×w_(256c),−n₁₆×w_(256c)),(n₂×w_(256c),−n₁₅×w_(256c)), (n₂×w_(256c),−n₁₄×w_(256c)),(n₂×w_(256c),−n₁₃×w_(256c)), (n₂×w_(256c),−n₁₂×w_(256c)),(n₂×w_(256c),−n₁₁×w_(256c)), (n₂×w_(256c),−n₁₀×w_(256c)),(n₂×w_(256c),−n₉×w_(256c)),(n₁×w_(256c),n₁₆×w_(256c)), (n₁×w_(256c),n₁₅×w_(256c)),(n₁×w_(256c),n₁₄×w_(256c)), (n₁×w_(256c),n₁₃×w_(256c)),(n₁×w_(256c),n₁₂×w_(256c)), (n₁×w_(256c),n₁₁×w_(256c)),(n₁×w_(256c),n₁₀×w_(256c)), (n₁×w_(256c), n₉×w_(256c)),(n₁×w_(256c),−n₁₆×w_(256c)), (n₁×w_(256c),−n₁₅×w_(256c)),(n₁×w_(256c),−n₁₄×w_(256c)), (n₁×w_(256c),−n₁₃×w_(256c)),(n₁×w_(256c),−n₁₂×w_(256c)), (n₁×w_(256c),−n₁₁×w_(256c)),(n₁×w_(256c),−n₁₀×w_(256c)), (n₁×w_(256c),−n₉×w_(256c)),(−n₈×w_(256c),n₁₆×w_(256c)), (−n₈×w_(256c),n₈×w_(256c)), (−n₈×w_(256c),n₁₄×w_(256c)), (−n₈×w_(256c),n₁₃×w_(256c)), (−n₈×w_(256c),n₁₂×w_(256c)),(−n₈×w_(256c),n₁₁×w_(256c)), (−n₈×w_(256c),n₁₀×w_(256c)),(−n₈×w_(256c),n₉×w_(256c)), (−n₈×w_(256c),−n₁₆×w_(256c)),(−n₈×w_(256c),−n₁₅×w_(256c)), (−n₈×w_(256c),−n₁₄×w_(256c)),(−n₈×w_(256c),−n₁₃×w_(256c)), (−n₈×w_(256c),−n₁₂×w_(256c)),(−n₈×w_(256c),−n₁₁×w_(256c)), (−n₈×w_(256c), −n₁₀×w_(256c)),(−n₈×w_(256c), −n₉×w_(256c)),(−n₇×w_(256c),n₁₆×w_(256c)), (−n₇×w_(256c),n₁₅×w_(256c)), (−n₇×w_(256c),n₁₄×w_(256c)), (−n₇×w_(256c),n₁₃×w_(256c)), (−n₇×w_(256c),n₁₂×w_(256c)),(−n₇×w_(256c),n₁₁×w_(256c)), (−n₇×w_(256c),n₁₀×w_(256c)),(−n₇×w_(256c),n₉×w_(256c)), (−n₇×w_(256c),−n₁₆×w_(256c)),(−n₇×w_(256c),−n₁₅×w_(256c)), (−n₇×w_(256c),−n₁₄×w_(256c)),(−n₇×w_(256c),−n₁₃×w_(256c)), (−n₇×w_(256c),−n₁₂×w_(256c)),(−n₇×w_(256c),−n₁₁×w_(256c)), (−n₇×w_(256c),−n₁₀×w_(256c)),(−n₇×w_(256c), −n₉×w_(256c)),(−n₆×w_(256c),n₁₆×w_(256c)), (−n₆×w_(256c),n₁₅×w_(256c)), (−n₆×w_(256c),n₁₄×w_(256c)), (−n₆×w_(256c),n₁₃×w_(256c)), (−n₆×w_(256c),n₁₂×w_(256c)), (−n₆×w_(256c), n₁₁×w_(256c)), (−n₆×w_(256c),n₁₀×w_(256c)), (−n₆×w_(256c), n₉×w_(256c)),(−n₆×w_(256c),−n₁₆×w_(256c)), (−n₆×w_(256c),−n₁₅×w_(256c)),(−n₆×w_(256c),−n₁₄×w_(256c)), (−n₆×w_(256c),−n₁₃×w_(256c)),(−n₆×w_(256c),−n₁₂×w_(256c)), (−n₆×w_(256c),−n₁₁×w_(256c)),(−n₆×w_(256c),−n₁₀×w_(256c)), (−n₆×w_(256c), −n₉×w_(256c)),(−n₅×w_(256c), n₁₆×w_(256c)), (−n₅×w_(256c),n₁₅×w_(256c)),(−n₅×w_(256c), n₁₄×w_(256c)), (−n₅×w_(256c),n₁₃×w_(256c)),(−n₅×w_(256c),n₁₂×w_(256c)), (−n₅×w_(256c),n₁₃×w_(256c)),(−n₅×w_(256c),n₁₀×w_(256c)), (−n₅×w_(256c),n₉×w_(256c)),(−n₅×w_(256c),−n₁₆×w_(256c)), (−n₅×w_(256c),−n₁₅×w_(256c)),(−n₁₅×w_(256c),−n₁₄×w_(256c)), (−n₅×w_(256c),−n₁₃×w_(256c)),(−n₅×w_(256c),−n₁₂×w_(256c)), (−n₅×w_(256c),−n₁₁×w_(256c)),(−n₅×w_(256c),−n₁₀×w_(256c)), (−n₅×w_(256c),−n₉×w_(256c)),(−n₄×w_(256c),n₁₆×w_(256c)), (−n₄×w_(256c),n₁₅×w_(256c)), (−n₄×w_(256c),n₁₄×w_(256c)), (−n₄×w_(256c),n₁₃×w_(256c)), (−n₄×w_(256c),n₁₂×w_(256c)),(−n₄×w_(256c),n₁₁×w_(256c)), (−n₄×w_(256c),n₁₀×w_(256c)),(−n₄×w_(256c),n₉×w_(256c)), (−n₄×w_(256c),−n₁₆×w_(256c)),(−n₄×w_(256c),−n₁₅×w_(256c)), (−n₄×w_(256c),−n₁₄×w_(256c)),(−n₄×w_(256c),−n₁₃×w_(256c)), (−n₄×w_(256c),−n₁₂×w_(256c)),(−n₄×w_(256c),−n₁₁×w_(256c)), (−n₄×w_(256c),−n₁₀×w_(256c)),(−n₄×w_(256c),n₉×w_(256c)),(−n₃×w_(256c), n₁₆×w_(256c)), (−n₃×w_(256c),n₁₅×w_(256c)),(−n₃×w_(256c), n₁₄×w_(256c)), (−n₃×w_(256c),n₁₃×w_(256c)),(−n₃×w_(256c), n₁₂×w_(256c)), (−n₃×w_(256c), n₁₁×w_(256c)),(−n₃×w_(256c), n₁₀×w_(256c)), (−n₃×w_(256c), n₉×w_(256c)),(−n₃×w_(256c),−n₁₆×w_(256c)), (−n₃×w_(256c),−n₁₅×w_(256c)),(−n₃×w_(256c),−n₁₄×w_(256c)), (−n₃×w_(256c),−n₁₃×w_(256c)),(−n₃×w_(256c),−n₁₂×w_(256c)), (−n₃×w_(256c),−n₁₁×w_(256c)),(−n₃×w_(256c), −n₁₀×w_(256c)), (−n₃×w_(256c), n₁₉×w_(256c)),(−n₂×w_(256c), n₁₆×w_(256c)), (−n₂×w_(256c),n₁₅×w_(256c)),(−n₂×w_(256c), n₁₄×w_(256c)), (−n₂×w_(256c),n₁₃×w_(256c)),(−n₂×w_(256c),n₁₂×w_(256c)), (−n₂×w_(256c),n₁₁×w_(256c)),(−n₂×w_(256c),n₁₀×w_(256c)), (−n₂×w_(256c),n₉×w_(256c)),(−n₂×w_(256c),−n₁₆×w_(256c)), (−n₂×w_(256c),−n₁₅×w_(256c)),(−n₂×w_(256c),−n₁₄×w_(256c)), (−n₂×w_(256c),−n₁₃×w_(256c)),(−n₂×w_(256c),−n₁₂×w_(256c)), (−n₂×w_(256c),−n₁₁×w_(256c)),(−n₂×w_(256c), −n₁₀×w_(256c)), (−n₂×w_(256c), −n₉×w_(256c)),(−n₁×w_(256c),n₁₆×w_(256c)), (−n₁×w_(256c),n₁₅×w_(256c)),(−n₁×w_(256c),n₁₄×w_(256c)), (−n₁×w_(256c),n₁₃×w_(256c)),(−n₁×w_(256c),n₁₂×w_(256c)), (−n₁×w_(256c), n₁₁×w_(256c)),(−n₁×w_(256c),n₁₀×w_(256c)), (−n₁×w_(256c), n₉×w_(256c)),(−n₁×w_(256c),−n₁₆×w_(256c)), (−n₁×w_(256c),−n₁₅×w_(256c)),(−n₁×w_(256c),−n₁₄×w_(256c)), (−n₁×w_(256c),−n₁₃×w_(256c)),(−n₁×w_(256c),−n₁₂×w_(256c)), (−n₁×w_(256c),−n₁₁×w_(256c)),(−n₁×w_(256c),−n₁₀×w_(256c)), (−n₁×w_(256c),−n₉×w_(256c)). Respectivecoordinates of the signal points (“◯”) immediately above the values00000000 to 11111111 of the set of b0, b1, b2, b3, b4, b5, b6, and b7 inthe I-Q plane serve as in-phase component I and quadrature component Qof the mapped baseband signal. The relationship between the set of b0,b1, b2, b3, b4, b5, b6, and b7 (00000000 to 11111111) and the signalpoint coordinates during 256QAM modulation is not limited to that inFIG. 121 .

256 signal points in FIG. 121 are named as “signal point 1”, “signalpoint 2”, . . . , “signal point 255”, and “signal point 256” (because ofthe presence of 256 signal points, “signal point 1” to “signal point256” exist). In the I-Q plane, Di is a distance between “signal point i”and the origin. At this point, w_(256c) is given by the followingequation.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 373} \right\rbrack & \; \\{w_{256\; c} = \frac{z}{\sqrt{\frac{\sum\limits_{i = 1}^{256}D_{i}^{2}}{256}}}} & ({H9})\end{matrix}$

Therefore, the mapped baseband signal has an average power of z₂. Theeffect is described later.

The effect of the use of QAM will be described below.

First, the configurations of the transmitter and receiver will bedescribed.

FIG. 117 illustrates a configuration example of the transmitter.Information 11701 is input to error correction encoder 11702, and errorcorrection encoder 11702 performs the error correction coding on theLDPC code or a turbo code, and outputs error-correction-coded data11703.

Error-correction-coded data 11703 is input to interleaver 11704, andinterleaver 11704 performs the data rearrangement, and outputs theinterleaved data 11705.

Interleaved data 11705 is input to mapper 11706, and mapper 11706performs the mapping based on the modulation scheme set with thetransmitter, and outputs quadrature baseband signal (in-phase componentI and quadrature component Q) 11707.

Quadrature baseband signal 11707 is input to radio section 11708, andradio section 11708 performs the pieces of processing such as thequadrature modulation, the frequency conversion, and the amplification,and outputs transmitted signal 11709.

Transmitted signal 11709 is output as a radio wave from antenna 11710.

FIG. 118 illustrates an example of the configuration of the receiverthat receives the modulated signal transmitted from the transmitter inFIG. 117 .

Received signal 11802 received with antenna 11801 is input to radiosection 11803, and radio section 11803 performs the pieces of processingsuch as the frequency conversion and the quadrature demodulation, andoutputs quadrature baseband signal 11804.

Quadrature baseband signal 11804 is input to demapper 11805, anddemapper 11805 performs the frequency offset estimation and removal andthe estimation of the channel variation (transmission path variation),estimates each bit of the data symbol, for example, the log-likelihoodratio, and outputs log-likelihood ratio signal 11806.

Log-likelihood ratio signal 11806 is input to deinterleaver 11807, anddeinterleaver 11807 performs the rearrangement, and outputsdeinterleaved log-likelihood ratio signal 11808.

Deinterleaved log-likelihood ratio signal 11808 is input to decoder11809, and decoder 11809 decodes the error correction code, and outputsreceived data 11810.

The effect will be described below with 16QAM as an example. Thefollowing two cases (<16QAM #3> and <16QAM #4>) are compared to eachother.

<16QAM #3>16QAM #1 is 16QAM described in (Supplement 2), and FIG. 111illustrates the arrangement of the signal points in the I-Q plane.

<16QAM #4> FIG. 119 illustrates the arrangement of the signal points inthe I-Q plane, and k₁>0 (k₁ is a real number larger than 0), k₂>0 (k₂ isa real number larger than 0), k₁≠1, k₂≠1, and k₁≠k₂ hold as describedabove.

As described above, four bits of b0, b1, b2, and b3 are transmitted in16QAM. For <16QAM #3>, in the receiver, the four bits are divided intotwo high-quality bits and two low-quality bits in the case that thelog-likelihood ratio of each bit is obtained. On the other hand, for<16QAM #4>, depending on the conditions of k₁>0 (k₁ is a real numberlarger than 0) and k₂>0 (k₂ is a real number larger than 0), k₁≠1, k₂≠1,and k₁≠k₂, the four bits are divided into one high-quality bit, twointermediate-quality bits, and one low-quality bit. Thus, the qualitydistribution of the 4 bits depends on the <16QAM #3> and <16QAM #4>. Atthis point, in the case that decoder 11809 in FIG. 118 decodes the errorcorrection code, depending on the error correction code used, thereceiver has a higher possibility of obtaining the high data receptionquality using <16QAM #4>.

In the case that the arrangement of the signal points are arranged inthe I-Q plane as illustrated in FIG. 120 for 64QAM, similarly thereceiver has the higher possibility of obtaining the high data receptionquality. At this point, as described above, it is assumed that “m₁>0 (m₁is a real number larger than 0) and m₂>0 (m₂ is a real number largerthan 0) and m₃>0 (m₃ is a real number larger than 0) and m₄>0 (m₄ is areal number larger than 0) and m₅>0 (m₅ is a real number larger than 0)and m₆>0 (m₆ is a real number larger than 0) and m₇>0 (m₇ is a realnumber larger than 0) and m₈>0 (m₈ is a real number larger than 0), and

{m₁≠m₂ and m₁≠m₃ and m₁≠m₄ and m₂≠m₃ and m₂≠m₄ and m₃≠m₄}

and

{m₅≠m₆ and m₅≠m₇ and m₅≠m₈ and m₆≠m₇ and m₆≠m₈ and m₇≠m₈}

and

{m₁≠m₅ or m₂≠m₆ or m₃≠m₇ or m₄≠m₈ holds}

hold.”

or

that “m₁>0 (m₁ is a real number larger than 0) and m₂>0 (m₂ is a realnumber larger than 0) and m₃>0 (m₃ is a real number larger than 0) andm₄>0 (m₄ is a real number larger than 0) and m₅>0 (m₅ is a real numberlarger than 0) and m₆>0 (m₆ is a real number larger than 0) and m₇>0 (m₇is a real number larger than 0) and m₈>0 (m₈ is a real number largerthan 0), and{m₁≠m₂ and m₁≠m₃ and m₁≠m₄ and m₂≠m₃ and m₂≠m₄ and m₃≠m₄}and{m₅+m₆ and m₅≠m₇ and m₅≠m₈ and m₆≠m₇ and m₆≠m₈ and m₇≠m₈}and{m₁≠m₅ or m₂≠m₆ or m₃≠m₇ or m₄≠m₈ holds}and{m₁=m₅ or m₂=m₆ or m₃=m₇ or m₄=m₈ holds}hold”, which necessary pointdiffers from that in the arrangement of the signal points of (Supplement2).

Similarly, in the case that the arrangement of the signal points arearranged in the I-Q plane as illustrated in FIG. 121 for 256QAM,similarly the receiver has the higher possibility of obtaining the highdata reception quality. At this point, as described above, it is assumedthat “n₁>0 (n₁ is a real number larger than 0) and n₂>0 (n₂ is a realnumber larger than 0) and n₃>0 (n₃ is a real number larger than 0) andn₄>0 (n₄ is a real number larger than 0) and n₅>0 (n₆ is a real numberlarger than 0) and n₇>0 (n₇ is a real number larger than 0) and n₅>0 (n₅is a real number larger than 0)

and n₉>0 (n₉ is a real number larger than 0) and n₁₀>0 (n₁₀ is a realnumber larger than 0) and n₁₁>0 (n₁₁ is a real number larger than 0) andn₁₂>0 (n₁₂ is a real number larger than 0) and n₁₃>0 (n₁₃ is a realnumber larger than 0) and n₁₄>0 (n₁₄ is a real number larger than 0) andn₁₅>0 (n₁₅ is a real number larger than 0) and n₁₆>0 (n₁₆ is a realnumber larger than 0), and{n₁≠n₂ and n₁≠n₃ and n₁≠n₄ and n₁≠n₅ and n₁≠n₆ and n₁≠n₇ and n₁≠n₈and n₂≠n₃ and n₂≠n₄ and n₂≠n₅ and n₂≠n₆ and n₂≠n₇ and n₂≠n₈and n₃≠n₄ and n₃≠n₅ and n₃≠n₆ and n₃≠n₇ and n₃≠n₈and n₄≠n₅ and n₄≠n₆ and n₄≠n₇ and n₄≠n₈and n₅≠n₆ and n₅≠n₇ and n₅+n₈and n₆≠n₇ and n₆≠n₈and n₇≠n₈}and{n₉≠n₁₀ and n₉≠n₁₁ and n₉≠n₁₂ and n₉≠n₁₃ and n₉≠n₁₄ and n₉≠n₁₅ andn₉≠n₁₆and n₁₀≠n₁₁ and n₁₀≠n₁₂ and n₁₀≠n₁₃ and n₁₀≠n₁₄ and n₁₀≠n₁₅ and n₁₀≠n₁₆and n₁₁≠n₁₂ and n₁₁≠n₁₃ and n₁₁≠n₁₄ and n₁₁≠n₁₅ and n₁₁≠n₁₆and n₁₂≠n₁₃ and n₁₂≠n₁₄ and n₁₂≠n₁₅ and n₁₂≠n₁₆and n₁₃≠n₁₄ and n₁₃≠n₁₅ and n₁₃≠n₁₆and n₁₄≠n₁₅ and n₁₄≠n₁₆and n₁₅≠n₁₆}and{n₁≠n₉ or n₂≠n₁₀ or n₃≠n₁₁ or n₄≠n₁₂ or n₅≠n₁₃ or n₆≠n₁₄ or n₇≠n₁₅ orn₈≠n₁₆ holds}hold.”orthat “n₁>0 (n₁ is a real number larger than 0) and n₂>0 (n₂ is a realnumber larger than 0) and n₃>0 (n₃ is a real number larger than 0) andn₄>0 (n₄ is a real number larger than 0) and n₅>0 (n₆ is a real numberlarger than 0) and n₇>0 (n₇ is a real number larger than 0) and n₈>0 (n₈is a real number larger than 0)and n_(9>0) (n₉ is a real number larger than 0) and n₁₀>0 (n₁₀ is a realnumber larger than 0) and n₁₁>0 (n₁₁ is a real number larger than 0) andn₁₂>0 (n₁₂ is a real number larger than 250) and n₁₃>0 (n₁₃ is a realnumber larger than 0) and n₁₄>0 (n₁₄ is a real number larger than 0) andn₁₅>0 (n₁₅ is a real number larger than 0) and n₁₆>0 (n₁₆ is a realnumber larger than 0), and{n₁≠n₂ and n₁≠n₃ and n₁≠n₄ and n₁≠n₅ and n₁≠n₆ and n₁≠n₇ and n₁≠n₅and n₂≠n₃ and n₂≠n₄ and n₂≠n₅ and n₂≠n₆ and n₂≠n₇ and n₂≠n₅and n₃≠n₄ and n₃≠n₅ and n₃≠n₆ and n₃≠n₇ and n₃≠n₈and n₄≠n₅ and n₄≠n₆ and n₄≠n₇ and n₄≠n₈and n₅≠n₆ and n₅≠n₇ and n₅≠n₈and n₆≠n₇ and n₆≠n₈and n₇≠n₈}and{n₉≠n₁₀ and n₉≠n₁₁ and n₉≠n₁₂ and n₉≠n₁₃ and n₉≠n₁₄ and n₉≠n₁₅ andn₉≠n₁₆and n₁₀≠n₁₁ and n₁₀≠n₁₂ and n₁₀≠n₁₃ and n₁₀≠n₁₄ and n₁₀≠n₁₅ and n₁₀≠n₁₆and n₁₁≠n₁₂ and n₁₁≠n₁₃ and n₁₁≠n₁₄ and n₁₁≠n₁₅ and n₁₁≠n₁₆and n₁₂≠n₁₃ and n₁₂≠n₁₄ and n₁₂≠n₁₅ and n₁₂≠n₁₆and n₁₃≠n₁₄ and n₁₃≠n₁₅ and n₁₃≠n₁₆and n₁₄≠n₁₅ and n₁₄≠n₁₆and n₁₅≠n₁₆}and{n₁≠n₉ or n₂≠n₁₀ or n₃≠n₁₁ or n₄≠n₁₂ or n₅≠n₁₃ or n₆≠n₁₄ or n₇≠n₁₅ orn₈≠n₁₆ holds}and{n₁=n₉ or n₂=n₁₀ or n₃=n₁₁ or n₄=n₁₂ or n₅=n₁₃ or n₆=n₁₄ or n₇=n₁₅ orn₈=n₁₆ holds}hold.”, which necessary point differs from that in thearrangement of the signal points of (Supplement 2).

Although the detailed configuration is not illustrated in FIGS. 117 and118 , similarly the modulated signal can be transmitted and receivedusing the OFDM scheme and spectral spread communication scheme, whichare described in another exemplary embodiment.

In the MIMO transmission scheme, the space-time codes such as thespace-time block code (however, the symbol mat be arranged on thefrequency axis), and the MIMO transmission scheme in which the precodingis performed or not performed, which are described in the first totwelfth exemplary embodiments, there is a possibility of improving thedata reception quality even if 16QAM, 64QAM, and 256QAM are used.

(Supplement 5)

A configuration example of a communication and broadcasting system inwhich QAM of (Supplement 2), (Supplement 3), and (Supplement 4) is usedwill be described below.

FIG. 122 illustrates an example of the transmitter. In FIG. 122 , thecomponent similarly to that in FIG. 117 is designated by the identicalreference mark.

Input signal 12201 is input to transmission method assigner 12202, andtransmission method assigner 12202 outputs information signal 12203associated with the error correction code (for example, the coding rateof the error correction code and the block length of the errorcorrection code), information signal 12204 associated with themodulation scheme (for example, the modulation scheme), and informationsignal 12205 of the parameter associated with the modulation scheme (forexample, information about an amplitude in QAM) in order to generate thedata symbol based on based on input signal 12201. A user who uses thetransmitter may generate input signal 12201, and feedback informationabout a communication partner communication may be used as input signal12201 when input signal 12201 is use in the communication system.

Information 11701 and information signal 12203 associated with the errorcorrection code are input to error correction encoder 11702, and errorcorrection encoder 11702 performs the error correction coding based oninformation signal 12203 associated with the error correction code, andoutputs error-correction-coded data 11703.

Interleaved data 11705, information signal 12204 associated with themodulation scheme, and information signal 12205 of the parameterassociated with the modulation scheme are input to mapper 11706, andmapper 11706 performs the mapping based on information signal 12204associated with the modulation scheme and information signal 12205 ofthe parameter associated with the modulation scheme, and outputsquadrature baseband signal 11707.

Information signal 12203 associated with the error correction code,information signal 12204 associated with the modulation scheme,information signal 12205 of the parameter associated with the modulationscheme, and control data 12206 are input to control information symbolgenerator 12207, and control information symbol generator 12207 performsthe error correction coding and the BPSK or QPSK modulation, and outputscontrol information symbol signal 12208.

Quadrature baseband signal 11707, control symbol signal 12208, pilotsymbol signal 12209, and frame configuration signal 12210 are input toradio section 11708, and radio section 11708 outputs transmitted signal11709 based on frame configuration signal 12210. FIG. 123 illustrates anexample of the frame configuration.

In the frame configuration of FIG. 123 , a vertical axis indicates thefrequency and a horizontal axis indicates the time. In FIG. 123 ,reference mark 12301 designates the pilot symbol, reference mark 12302designates the control information symbol, and reference mark 12303designates the data symbol. Pilot symbol 12301 corresponds to pilotsymbol signal 12209 in FIG. 122 , control information symbol 12302corresponds to control information symbol signal 12208 in FIG. 122 , anddata symbol 12303 corresponds to quadrature baseband signal 11707 inFIG. 122 .

FIG. 124 illustrates an example of the receiver that receives themodulated signal transmitted from the transmitter in FIG. 122 . In FIG.124 , the component similarly to that in FIG. 118 is designated by theidentical reference mark.

Quadrature baseband signal 11804 is input to synchronizer 12405, andsynchronizer 12405 performs the frequency synchronization, the timesynchronization, and the frame synchronization by detecting and usingpilot symbol 12301 in FIG. 123 , and outputs synchronization signal12406.

Quadrature baseband signal 11804 and synchronization signal 12406 areinput to control information demodulator 12401, and control informationdemodulator 12401 demodulates control information symbol 12302 in FIG.123 (and the error correction decoding), and outputs control informationsignal 12402.

Quadrature baseband signal 11804 and synchronization signal 12406 areinput to frequency offset and transmission path estimator 12403, andfrequency offset and transmission path estimator 12403 estimates afrequency offset and a transmission path variation caused by a currentusing pilot symbol 12301 in FIG. 123 , and outputs frequency offset andtransmission path variation estimated signal 12404.

Quadrature baseband signal 11804, control information signal 12402,frequency offset and transmission path variation estimated signal 12404,and synchronization signal 12406 are input to demapper 11805, anddemapper 11805 determines the modulation scheme of data symbol 12303 inFIG. 123 using control information signal 12402, obtains thelog-likelihood ratio of each bit in the data symbol using quadraturebaseband signal 12403 and frequency offset and transmission pathvariation estimated signal 12404, and outputs log-likelihood ratiosignal 11806.

Log-likelihood ratio signal 11808 and control information signal 12402are input to deinterleaver 11807, and deinterleaver 11807 performsprocessing for the deinterleaving method corresponding to theinterleaving method used in the transmitter from the information aboutthe transmission method, such as the modulation scheme and the errorcorrection coding scheme, which is included in control informationsignal 12402, and outputs deinterleaved log-likelihood ratio signal11808.

Deinterleaved log-likelihood ratio signal 11808 and control informationsignal 12402 are input to decoder 11809, and decoder 11809 performs theerror correction decoding from the error correction coding schemeincluded in the control information, and outputs received data 11810.

Examples in which QAM of (Supplement 2), (Supplement 3), and (Supplement4) is used will be described below.

Example 1

It is assumed that the transmitter in FIG. 122 can transmit theplurality of block lengths (code lengths) as the error correction code.

For example, it is assumed that the transmitter in FIG. 122 selects oneof the error correction coding with the LDPC (block) code having theblock length (code length) of 16200 bits and the error correction codingwith the LDPC (block) code having the block length (code length) 64800bits to performs the error correction code. Accordingly, the followingtwo error correction schemes are considered.

<Error Correction Scheme #1>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 16200 bits (information:10800 bits and parity: 5400 bits).

<Error Correction Scheme #2>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 64800 bits (information:43200 bits and parity: 21600 bits).

It is assumed that 16QAM in FIG. 111 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets f=f_(#1) in FIG.111 using <error correction scheme #1>, and sets f=f_(#2) in FIG. 111using <error correction scheme #2>. At this point,

<Condition #H1>

f_(#1)≠1 and f_(#2)≠1 and f_(#1)≠f_(#2) preferably hold. Therefore, thereceiver has a higher possibility of obtaining the high data receptionquality in both <error correction scheme #1> and <error correctionscheme #2> (because <error correction scheme #1> differs from <errorcorrection scheme #2> in a suitable value of f).

It is assumed that 64QAM in FIG. 112 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets g₁=g_(1,#1),g₂=g_(2,#1), and g₃=g_(3,#1) in FIG. 112 using <error correction scheme#1>, and sets g₁=g_(1,#2), g₂=g_(2,#2), and g₃=g_(3,#2) in FIG. 112using <error correction scheme #2>. Therefore, the following conditionpreferably holds.

<Condition #H2>

{(g_(1,#1),g_(2,#1),g_(3,#1))≠(1,3,5) and(g₁,#₁,g_(2,#1),g_(3,#1))≠(1,5,3) and(g_(1,#1),g_(2,#1),g_(3,#1))≠(3,1,5) and(g_(1,#1),g_(2,#1),g_(3,#1))+(3,5,1) and(g_(1,#1),g_(2,#1),g_(3,#1))+(5,1,3) and(g_(1,#1),g_(2,#1),g_(3,#1))+(5,3,1)}

and

{(g_(1,#2),g_(2,#2),g_(3,#2))+(1,3,5) and(g_(1,#2),g_(2,#2),g_(3,#2))≠(1,5,3) and(g_(1,#2),g_(2,#2),g_(3,#2))≠(3,1,5) and(g_(1,#2),g_(2,#2),g_(3,#2))≠(3,5,1) and(g_(1,#2),g_(2,#2),g_(3,#2))≠(5,1,3) and(g_(1,#2),g_(2,#2),g_(3,#2))≠(5,3,1)}

and

{{g_(1,#1)≠g_(1,#2) or g_(2,#1)≠g_(2,#2) or g_(3,#1)≠g_(3,#2)} holds}

hold.

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #1> and <errorcorrection scheme #2> (because <error correction scheme #1> differs from<error correction scheme #2> in a suitable set of g₁, g₂, and g₃).

It is assumed that 256QAM in FIG. 113 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1), andh₇=h_(7,#1) in FIG. 113 using <error correction scheme #1>, and setsh₁=h_(1,#2), h₂=h_(2,#2), h₃=h_(3,#2), h₄=h_(4,#2), h₅=h_(5,#2),h₆=h_(6,#2), and h₇=h_(7,#2) in FIG. 113 using <error correction scheme#2>. Therefore, the following condition preferably holds.

<Condition #H3>

{When {a1 is an integer from 1 to 7 and a2 is an integer from 1 to 7 anda3 is an integer from 1 to 7 and a4 is an integer from 1 to 7 and a5 isan integer from 1 to 7 and a6 is an integer from 1 to 7 and a7 is aninteger from 1 to 7} and {x is an integer from 1 to 7 and y is aninteger from 1 to 7 and x≠y} and {ax≠ay holds for all values x and y}hold, (h_(a1,#1), h_(a2,#1), h_(a3,#1), h_(a4,#1), h_(a5,#1), h_(a6,#1),h_(a7,#1))+(1,3,5,7,9,11,13) holds},

and

{when {a1 is an integer from 1 to 7 and a2 is an integer from 1 to 7 anda3 is an integer from 1 to 7 and a4 is an integer from 1 to 7 and a5 isan integer from 1 to 7 and a6 is an integer from 1 to 7 and a7 is aninteger from 1 to 7} and {x is an integer from 1 to 7 and y is aninteger from 1 to 7 and x≠y} and {ax≠ay holds for all values x and y}hold, (h_(a1,#2), h_(a2,#2), h_(a3,#2), h_(a4,#2), h_(a5,#2), h_(a6,#2),h_(a7,#2))+(1,3,5,7,9,11,13) holds}and{{h_(1,#1)≠h_(1,#2) or h_(2,#1)≠h_(2,#2) or h_(3,#1)≠h_(3,#2) orh_(4,#1)≠h_(4,#2) or h_(5,#1)≠h_(5,#2) or h_(6,#1)≠h_(6,#2) or h_(7,#1)≠h_(7,#2)} holds}hold.

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #1> and <errorcorrection scheme #2> (because <error correction scheme #1> differs from<error correction scheme #2> in a suitable set of h₁, h₂, h₃, h₄, h₅,h₆, and h₇).

The following is a summary of the above.

The following two error correction schemes are considered.

<Error Correction Scheme #1*>

The coding is performed using the block code having coding rate A andthe block length (code length) of B bits (A is a real number, 0<A<1holds, and B is an integer larger than 0).

<Error Correction Scheme #2*>

The coding is performed using the block code having coding rate A andthe block length (code length) of C bits (A is a real number, 0<A<1holds, C is an integer larger than 0, and B≠C holds).

It is assumed that 16QAM in FIG. 111 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets f=f_(#1) in FIG.111 using <error correction scheme #1*>, and sets f=f_(#2) in FIG. 111using <error correction scheme #2*>. At this point, <Condition #H1>preferably holds.

It is assumed that 64QAM in FIG. 112 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets g₁=g_(1,#1),g₂=g_(2,#1), and g₃=g_(3,#1) in FIG. 112 using <error correction scheme#1*>, and sets g₁=g_(1,#2), g₂=g_(2,#2), and g₃=g_(3,#2) in FIG. 112using <error correction scheme #2*>. At this point, <Condition #H2>preferably holds.

It is assumed that 256QAM in FIG. 113 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1), andh₇=h_(7,#1) in FIG. 113 using <error correction scheme #1*>, and setsh₁=h_(1,#2), h₂=h_(2,#2), h₃=h_(3,#2), h₄=h_(4,#2), h₅=h_(5,#2),h₆=h_(6,#2), and h₇=h_(7,#2) in FIG. 112 using <error correction scheme#2*>. At this point, <Condition #H3> preferably holds.

Example 2

It is assumed that the transmitter in FIG. 122 can transmit theplurality of block lengths (code lengths) as the error correction code.

For example, it is assumed that the transmitter in FIG. 122 selects oneof the error correction coding with the LDPC (block) code having theblock length (code length) of 16200 bits and the error correction codingwith the LDPC (block) code having the block length (code length) 64800bits to performs the error correction code. Accordingly, the followingtwo error correction schemes are considered.

<Error Correction Scheme #3>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 16200 bits (information:10800 bits and parity: 5400 bits).

<Error Correction Scheme #4>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 64800 bits (information:43200 bits and parity: 21600 bits).

It is assumed that 16QAM in FIG. 114 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets f₁=f_(1,#1) andf₂=f_(2,#1) in FIG. 114 using <error correction scheme #3>, and setsf₁=f_(1,#2) and f₂=f_(2,#2) in FIG. 114 using <error correction scheme#4>. At this point,

<Condition #H4>

{f_(1,#1)+f_(1,#2) or f_(2,#1)≠f_(2,#2)} preferably holds. Therefore,the receiver has a higher possibility of obtaining the high datareception quality in both <error correction scheme #1> and <errorcorrection scheme #3> (because <error correction scheme #3> differs from<error correction scheme #4> in a suitable set of f₁ and f₂).

It is assumed that 64QAM in FIG. 115 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets g₁=g_(1,#1),g₂=g_(2,#1), g₃=g_(3,#1), g₄=g_(4,#1), g₅=g_(5,#1), and g₆=g_(6,#1) inFIG. 115 using <error correction scheme #3>, and sets g₁=g_(1,#2),g₂=g_(2,#2), g₃=g_(3,#2), g₄=g_(4,#2), g₅=g_(5,#2), and g₆=g_(6,#2) inFIG. 115 using <error correction scheme #4>. Therefore, the followingcondition preferably holds.

<Condition #H5>

 {  {{g_(1,#1) ≠ g_(1,#2) and g_(1,#1) ≠ g_(2,#2) and g_(1,#1) ≠g_(3,#2)} or {g_(2,#1) ≠ g_(1,#2) and g_(2,#1) ≠ g_(2,#2) and g_(2,#1) ≠g_(3,#2)} or {g_(3,#1) ≠ g_(1,#2) and g_(3,#1) ≠ g_(2,#2) and g_(3,#1) ≠g_(3,#2)} holds} or {{g_(4,#1) ≠ g_(4,#2) and g_(4,#1) ≠ g_(5,#2) andg_(4,#1) ≠ g_(6,#2)} or {g_(5,#1) ≠ g_(4,#2) and g_(5,#1) ≠ g_(5,#2) andg_(5,#1) ≠ g_(6,#2)} or {g_(6,#1) ≠ g_(4,#2) and g_(6,#1) ≠ g_(5,#2) andg_(6,#1) ≠ g_(6,#2)} holds} } holds.

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #3> and <errorcorrection scheme #4> (because <error correction scheme #3> differs from<error correction scheme #4> in a suitable set of g₁, g₂, g₃, g₄, g₅,and g₆).

It is assumed that 256QAM in FIG. 116 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1),h₇=h_(7,#1), h₈=h_(8,#1), h₉=h_(9,#1), h₁₀=h_(10,#1), h₁₁=h_(11,#1),h₁₂=h_(12,#1), h₁₃=h_(13,#1), and h₁₄=h_(14,#1) in FIG. 116 using <errorcorrection scheme #3>, and sets h₁=h_(1,#2), h₂=h_(2,#2), h₃=h_(3,#2),h₄=h_(4,#2), h₅=h_(5,#2), h₆=h_(6,#2), h₇=h_(7,#2), h₈=h_(8,#2),h₉=h_(9,#2), h₁₀=h_(10,#2), h₁₁=h_(11,#2), h₁₂=h_(12,#2), h₁₃=h_(13,#2),and h₁₄=h_(14,#2) in FIG. 116 using <error correction scheme #4>.Therefore, the following condition preferably holds.

<Condition #H6>

{ {k is an integer from 1 to 7, and h_(1,#1) ≠ h_(k,#2) holds for allthe value of k} or {k is an integer from 1 to 7, and h_(2,#1) ≠ h_(k,#2)holds for all the value of k} or {k is an integer from 1 to 7, andh_(3,#1) ≠ h_(k,#2) holds for all the value of k} or {k is an integerfrom 1 to 7, and h_(4,#1) ≠ h_(k,#2) holds for all the value of k} or {kis an integer from 1 to 7, and h_(5,#1) ≠ h_(k,#2) holds for all thevalue of k} or {k is an integer from 1 to 7, and h_(6,#1) ≠ h_(k,#2)holds for all the value of k} or {k is an integer from 1 to 7, andh_(7,#1) ≠ h_(k,#2) holds for all the value of k} } or { {k is aninteger from 8 to 14, and h_(8,#1) ≠ h_(k,#2) holds for all the value ofk} or {k is an integer from 8 to 14, and h_(9,#1) ≠ h_(k,#2) holds forall the value of k} or {k is an integer from 8 to 14, and h_(10,#1) ≠h_(k,#2) holds for all the value of k} or {k is an integer from 8 to 14,and h_(11,#1) ≠ h_(k,#2) holds for all the value of k} or {k is aninteger from 8 to 14, and h_(12,#1) ≠ h_(k,#2) holds for all the valueof k} or {k is an integer from 8 to 14, and h_(13,#1) ≠ h_(k,#2) holdsfor all the value of k} or {k is an integer from 8 to 14, and _(h14,#1)≠ h_(k,#2) holds for all the value of k} }

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #3> and <errorcorrection scheme #4> (because <error correction scheme #3> differs from<error correction scheme #4> in a suitable set of h₁, h₂, h₃, h₄, h₅,h₆, h₇, h₈, h₉, h₁₀, h₁₁, h₁₂, h₁₃, and h₁₄).

The following is a summary of the above.

The following two error correction schemes are considered.

<Error Correction Scheme #3*>

The coding is performed using the block code having coding rate A andthe block length (code length) of B bits (A is a real number, 0<A<1holds, and B is an integer larger than 0).

<Error Correction Scheme #4*>

The coding is performed using the block code having coding rate A andthe block length (code length) of C bits (A is a real number, 0<A<1holds, C is an integer larger than 0, and B≠C holds).

It is assumed that 16QAM in FIG. 114 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets f₁=f_(1,#1) andf₂=f_(2,#1) in FIG. 114 using <error correction scheme #3*>, and setsf₁=f_(1,#2) and f₂=f_(2,#2) in FIG. 114 using <error correction scheme#4*>. At this point, <Condition #H4> preferably holds.

It is assumed that 64QAM in FIG. 115 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets g₁=g_(1,#1),g₂=g_(2,#1), g₃=g_(3,#1), g₄=g_(4,#1), g₅=g_(5,#1), and g₆=g_(6,#1) inFIG. 115 using <error correction scheme #3*>, and sets g₁=g_(1,#2),g₂=g_(2,#2), g₃=g_(3,#2), g₄=g_(4,#2), g₅=g_(5,#2), and g₆=g_(6,#2) inFIG. 115 using <error correction scheme #4*>. At this point, <Condition#H5> preferably holds.

It is assumed that 256QAM in FIG. 116 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1), andh₇=h_(7,#1) in FIG. 116 using <error correction scheme #3*>, and setsh₁=h_(1,#2), h₂=h_(2,#2), h₃=h_(3,#2), h₄=h_(4,#2), h₅=h_(5,#2),h₆=h_(6,#2), and h₇=h_(7,#2) in FIG. 116 using <error correction scheme#4*>. At this point, <Condition #H6> preferably holds.

Example 3

It is assumed that the transmitter in FIG. 122 can transmit theplurality of block lengths (code lengths) as the error correction code.

For example, it is assumed that the transmitter in FIG. 122 selects oneof the error correction coding with the LDPC (block) code having theblock length (code length) of 16200 bits and the error correction codingwith the LDPC (block) code having the block length (code length) 64800bits to performs the error correction code. Accordingly, the followingtwo error correction schemes are considered.

<Error Correction Scheme #5>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 16200 bits (information:10800 bits and parity: 5400 bits).

<Error Correction Scheme #6>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 64800 bits (information:43200 bits and parity: 21600 bits).

It is assumed that 16QAM in FIG. 119 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets k₁=k_(1,#1) andk₂=k_(2,#1) in FIG. 119 using <error correction scheme #5>, and setsk₁=k_(1,#2) and k₂=k_(2,#2) in FIG. 119 using <error correction scheme#6>. At this point,

<Condition #H7>

{k_(1,#1)≠k_(1,#2) or k_(2,#1)≠k_(2,#2)} preferably holds. Therefore,the receiver has a higher possibility of obtaining the high datareception quality in both <error correction scheme #5> and <errorcorrection scheme #6> (because <error correction scheme #5> differs from<error correction scheme #6> in a suitable set of k₁ and k₂).

It is assumed that 64QAM in FIG. 120 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets m₁=m_(1,#1),m₂=m_(2,#1), m₃=m_(3,#1), m₄=m_(4,#1), m₅=m_(5,#1), m₆=m_(6,#1),m₇=m_(7,#1), and m₈=m_(8,#1) in FIG. 120 using <error correction scheme#5>, and sets m₁=m_(1,#2), m₂=m_(2,#2), m₃=m_(3,#2), m₄=m_(4,#2),m₅=m_(5,#2), m₆=m_(6,#2), m₇=m_(7,#2), and m₈=m_(8,#2) in FIG. 120 using<error correction scheme #6>. Therefore, the following conditionpreferably holds.

<Condition #H8>

{ {{m_(1,#1) ≠ m_(1,#2) and m_(1,#1) ≠ m_(2,#2) and m_(1,#1) ≠ m_(3,#2)and m_(1,#1) ≠ m_(4,#2)} or {m_(2,#1) ≠ m_(1,#2) and m_(2,#1) ≠ m_(2,#2)and m_(2,#1) ≠ m_(3,#2) and m_(2,#1) ≠ m_(4,#2)} or {m_(3,#1) ≠ m_(1,#2)and m_(3,#1) ≠ m_(2,#2) and m_(3,#1) ≠ m_(3,#2) and m_(3,#1) ≠ m_(4,#2)}or {m_(4,#1) ≠ m_(1,#2) and m_(4,#1) ≠ m_(2,#2) and m_(4,#1) ≠ m_(3,#2)and m_(4,#1) ≠ m_(4,#2)} holds} or {{m_(5,#1) ≠ m_(5,#2) and m_(5,#1) ≠m_(6,#2) and m_(5,#1) ≠ m_(7,#2) and m_(5,#1) ≠ m_(8,#2)} or {m_(6,#1) ≠m_(5,#2) and m_(6,#1) ≠ m_(6,#2) and m_(6,#1) ≠ m_(7,#2) and m_(6,#1) ≠m_(8,#2)} or {m_(7,#1) ≠ m_(5,#2) and m_(7,#1) ≠ m_(6,#2) and m_(7,#1) ≠m_(7,#2) and m_(7,#1) ≠ m_(8,#2)} or {m_(8,#1) ≠ m_(5,#2) and m_(8,#1) ≠m_(6,#2) and m_(8,#1) ≠ m_(7,#2) and m_(8,#1) ≠ m_(8,#2)} holds} }holds.

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #5> and <errorcorrection scheme #6> (because <error correction scheme #5> differs from<error correction scheme #6> in a suitable set of m₁, m₂, m₃, m₄, m₅,m₆, m₇, and m₈).

It is assumed that 256QAM in FIG. 121 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets n₁=n_(1,#1),n₂=n_(2,#1), n₃=n_(3,#1), n₄=n_(4,#1), n₅=n_(5,#1), n₆=n_(6,#1),n₇=n_(7,#1), n₈=n_(8,#1), n₉=n_(9,#1), n₁₀=n_(10,#1), n₁₁=n_(11,#1),n₁₂=n_(12,#1), n₁₃=n_(13,#1), n₁₄=n_(14,#1), n₁₅=n_(15,#1), andn₁₆=n_(16,#1) in FIG. 121 using <error correction scheme #5>, and setsn₁=n_(1,#2), n₂=n_(2,#2), n₃=n_(3,#2), n₄=n_(4,#2), n₅=n_(5,#2),n₆=n_(6,#2), n₇=n_(7,#2), n₈=n_(8,#2), n₉=n_(9,#2), n₁₀=n_(10,#2),n₁₁=n_(11,#2), n₁₂=n_(12,#2), n₁₃=n_(13,#2), n₁₄=n_(14,#2),n₁₅=n_(15,#2), and n₁₆=n_(16,#2) in FIG. 121 using <error correctionscheme #6>. Therefore, the following condition preferably holds.

<Condition #H9>

{ {k is an integer from 1 to 8, and n_(1,#1) ≠ n_(k,#2) holds for allthe value of k} or {k is an integer from 1 to 8, and n_(2,#1) ≠ n_(k,#2)holds for all the value of k} or {k is an integer from 1 to 8, andn_(3,#1) ≠ n_(k,#2) holds for all the value of k} or {k is an integerfrom 1 to 8, and n_(4,#1) ≠ n_(k,#2) holds for all the value of k} or {kis an integer from 1 to 8, and n_(5,#1) ≠ n_(k,#2) holds for all thevalue of k} or {k is an integer from 1 to 8, and n_(6,#1) ≠ n_(k,#2)holds for all the value of k} or {k is an integer from 1 to 8, andn_(7,#1) ≠ n_(k,#2) holds for all the value of k} or {k is an integerfrom 1 to 8, and n_(8,#1) ≠ n_(k,#2) holds for all the value of k} } or{ {k is an integer from 9 to 16, and n_(9,#1) ≠ n_(k,#2) holds for allthe value of k} or {k is an integer from 9 to 16, and n_(10,#1) ≠n_(k,#2) holds for all the value of k} or {k is an integer from 9 to 16,and n_(11,#1) ≠ n_(k,#2) holds for all the value of k} or {k is aninteger from 9 to 16, and n_(12,#1) ≠ n_(k,#2) holds for all the valueof k} or {k is an integer from 9 to 16, and n_(13,#1) ≠ n_(k,#2) holdsfor all the value of k} or {k is an integer from 9 to 16, and n_(14,#1)≠ n_(k,#2) holds for all the value of k} or {k is an integer from 9 to16, and n_(15,#1) ≠ n_(k,#2) holds for all the value of k} or {k is aninteger from 9 to 16, and n_(16,#1) ≠ n_(k,#2) holds for all the valueof k} }

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #5> and <errorcorrection scheme #6> (because <error correction scheme #5> differs from<error correction scheme #6> in a suitable set of n₁, n₂, n₃, n₄, n₅,n₆, n₇, n₈, n₉, n₁₀, n₁₁, n₁₂, n₁₃, n₁₄, n₁₅, and n₁₆).

The following is a summary of the above.

The following two error correction schemes are considered.

<Error Correction Scheme #5*>

The coding is performed using the block code having coding rate A andthe block length (code length) of B bits (A is a real number, 0<A<1holds, and B is an integer larger than 0).

<Error Correction Scheme #6*>

The coding is performed using the block code having coding rate A andthe block length (code length) of C bits (A is a real number, 0<A<1holds, C is an integer larger than 0, and B≠C holds).

It is assumed that 16QAM in FIG. 119 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets k₁=k_(1,#1) andk₂=k_(2,#1) in FIG. 119 using <error correction scheme #5*>, and setsk₁=k_(1,#2) and k₂=k_(2,#2) in FIG. 119 using <error correction scheme#6*>. At this point, <Condition #H7> preferably holds.

It is assumed that 64QAM in FIG. 120 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets m₁=m_(1,#1),m₂=m_(2,#1), m₃=m_(3,#1), m₄=m_(4,#1), m₅=m_(5,#1), m₆=m_(6,#1),m₇=m_(7,#1), and m₈=m_(8,#1) in FIG. 120 using <error correction scheme#5*>, and sets m₁=m_(1,#2), m₂=m_(2,#2), m₃=m_(3,#2), m₄=m_(4,#2),m₅=m_(5,#2), m₆=m_(6,#2), m₇=m_(7,#2), and m₈=m_(8,#2) in FIG. 120 using<error correction scheme #6*>. At this point, <Condition #H8> preferablyholds.

It is assumed that 256QAM in FIG. 121 is used in the transmitter in FIG.122 . At this point, the transmitter in FIG. 122 sets n₁=n_(1,#1),n₂=n_(2,#1), n₃=n_(3,#1), n₄=n_(4,#1), n₅=n_(5,#1), n₆=n_(6,#1),n₇=n_(7,#1), n₈=n_(8,#1), n₉=n_(9,#1), n₁₀=n_(10,#1), n₁₁=n_(11,#1),n₁₂=n_(12,#1), n₁₃=n_(13,#1), n₁₄=n_(14,#1), n₁₅=n_(15,#1), andn₁₆=n_(16,#1) in FIG. 121 using <error correction scheme #5*>, and setsn₁=n_(1,#2), n₂=n_(2,#2), n₃=n_(3,#2), n₄=n_(4,#2), n₅=n_(5,#2),n₆=n_(6,#2), n₇=n_(7,#2), n₈=n_(8,#2), n₉=n_(9,#2), n₁₀=n_(10,#2),n₁₁=n_(11,#2), n₁₂=n_(12,#2), n₁₃=n_(13,#2), n₁₄=n_(14,#2),n₁₅=n_(15,#2), and n₁₆=n_(16,#2) in FIG. 121 using <error correctionscheme #6*>. At this point, <Condition #H9> preferably holds.

Although the detailed configuration is not illustrated in FIGS. 122 and124 , similarly the modulated signal can be transmitted and receivedusing the OFDM scheme and spectral spread communication scheme, whichare described in another exemplary embodiment.

In the MIMO transmission scheme, the space-time codes such as thespace-time block code (however, the symbol mat be arranged on thefrequency axis), and the MIMO transmission scheme in which the precodingis performed or not performed, which are described in the first totwelfth exemplary embodiments, there is a possibility of improving thedata reception quality even if 16QAM, 64QAM, and 256QAM are used.

As described above, when the transmitter performs the modulation(mapping) to transmit the modulated signal, the transmitter transmitsthe control information such that the receiver can identify themodulation scheme and the parameters of the modulation scheme, whichallows the receiver in FIG. 124 to perform the demapping (demodulation)by obtaining the control information.

(Supplement 6)

A configuration example of a communication and broadcasting system inwhich QAM of (Supplement 2), (Supplement 3), and (Supplement 4),particularly the MIMO transmission scheme is used will be describedbelow.

FIG. 125 illustrates an example of the transmitter. In FIG. 125 , thecomponent similarly to that in FIG. 122 is designated by the identicalreference mark.

Input signal 12201 is input to transmission method assigner 12202, andtransmission method assigner 12202 outputs information signal 12203associated with the error correction code (for example, the coding rateof the error correction code and the block length of the errorcorrection code), information signal 12204 associated with themodulation scheme (for example, the modulation scheme), informationsignal 12205 of the parameter associated with the modulation scheme (forexample, information about an amplitude in QAM), and information signal12505 associated with the transmission method (the information about theMIMO transmission, the single stream transmission, and the MISOtransmission (the transmission with the space-time block cod)) in orderto generate the data symbol based on based on input signal 12201. A userwho uses the transmitter may generate input signal 12201, and feedbackinformation about a communication partner communication may be used asinput signal 12201 when input signal 12201 is use in the communicationsystem. It is assumed that the MIMO transmission, the single streamtransmission, and the MISO transmission (the transmission with thespace-time block cod) can be assigned as the transmission method, andthat the transmission method in which the precoding and phase change ofthe first to twelfth exemplary embodiments are performed is dealt withas the MIMO transmission.

Information 11701 and information signal 12203 associated with the errorcorrection code are input to error correction encoder 11702, and errorcorrection encoder 11702 performs the error correction coding based oninformation signal 12203 associated with the error correction code, andoutputs error-correction-coded data 11703.

Error-correction-coded data 11703, information signal 12204 associatedwith the modulation scheme, information signal 12205 of the parameterassociated with the modulation scheme, and information signal 12505associated with the transmission method are input to signal processor12501, and signal processor 12501 performs the pieces of processing suchas the interleaving, the mapping, the precoding, the phase change, andthe power change on error-correction-coded data 11703 based on theinformation signals, and outputs post-processing baseband signals 12502Aand 12502B.

Information signal 12203 associated with the error correction code,information signal 12204 associated with the modulation scheme,information signal 12205 of the parameter associated with the modulationscheme, control data 12206, and information signal 12505 associated withthe transmission method are input to control information symbolgenerator 12207, and control information symbol generator 12207 performsthe error correction coding and the BPSK or QPSK modulation, and outputscontrol information symbol signal 12208.

Post-processing baseband signal 12502A, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503Λ, and radio section 12503Λ outputstransmitted signal 12504A as the radio wave from antenna #1 (12505A)based on frame configuration signal 12210. FIG. 126 illustrates anexample of the frame configuration.

Post-processing baseband signal 12502B, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503B, and radio section 12503B outputstransmitted signal 12504B as the radio wave from antenna #2 (12505B)based on frame configuration signal 12210. FIG. 126 illustrates anexample of the frame configuration.

The operation of signal processor 12501 in FIG. 125 will be describedbelow with reference to FIG. 126 .

In the frame configuration of FIG. 126 , a vertical axis indicates thefrequency and a horizontal axis indicates the time. In FIG. 126 , (a)illustrates the frame configuration of the signal transmitted fromantenna #1 (12505A) in FIG. 125 , and (b) illustrates the frameconfiguration of the signal transmitted from antenna #2 (12505B) in FIG.125 .

First, the operation of the transmitter that transmits pilot symbol12601, control information symbol 12602, and data symbol 12603 in FIG.126 will be described.

As to the transmission scheme, one-stream modulated signal istransmitted from the transmitter in FIG. 125 . At this point, forexample, first and second methods are considered.

First Method:

Error-correction-coded data 11703, information signal 12204 associatedwith the modulation scheme, information signal 12205 of the parameterassociated with the modulation scheme, and information signal 12505associated with the transmission method are input to signal processor12501, and signal processor 12501 decides the modulation schemeaccording to information signal 12204 associated with the modulationscheme and information signal 12205 of the parameter associated with themodulation scheme, performs the mapping according to the decidedmodulation scheme, and outputs post-processing baseband signal 12502A.At this point, it is assumed that post-processing baseband signal 12502Bis not output (it is assumed that signal processor 12501 performs theprocessing such as the interleaving).

Post-processing baseband signal 12502A, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503Λ, and radio section 12503Λ outputstransmitted signal 12504A as the radio wave from antenna #1 (12505A)based on frame configuration signal 12210. It is assumed that the radiosection 12503B is not operated and therefore the radio wave is notoutput from antenna #2 (12505B).

As to the transmission scheme, the second method in which one-streammodulated signal is transmitted from the transmitter in FIG. 125 will bedescribed below.

Second Method:

Error-correction-coded data 11703, information signal 12204 associatedwith the modulation scheme, information signal 12205 of the parameterassociated with the modulation scheme, and information signal 12505associated with the transmission method are input to signal processor12501, and signal processor 12501 decides the modulation schemeaccording to information signal 12204 associated with the modulationscheme and information signal 12205 of the parameter associated with themodulation scheme, performs the mapping according to the decidedmodulation scheme, and generates the mapped signal.

Signal processor 12501 generates the signals of two series based on themapped signal, and outputs the signals as post-processing basebandsignals 12502A and 12502B. The term “generating the signals of twoseries based on the mapped signal” means that the signals of two seriesare generated based on the mapped signal by performing the phase changeor the power change on the mapped signal (as described above, it isassumed that signal processor 12501 performs the processing such as theinterleaving).

Post-processing baseband signal 12502A, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503Λ, and radio section 12503Λ outputstransmitted signal 12504A as the radio wave from antenna #1 (12505A)based on frame configuration signal 12210.

Post-processing baseband signal 12502B, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503B, and radio section 12503B outputstransmitted signal 12504B as the radio wave from antenna #2 (12505B)based on frame configuration signal 12210.

The operation of the transmitter that transmits pilot symbols 12604A and12604B, control information symbols 12605A and 12605B, and data symbols12606A and 12606B in FIG. 126 will be described below.

Pilot symbols 12604A and 12604B are transmitted from the transmitter attime Y1 using the identical frequency (common frequency).

Similarly, control information symbols 12505A and 12605B are transmittedfrom the transmitter at time Y2 using the identical frequency (commonfrequency).

Data symbols 12606A and 12606B are transmitted from the transmitterbetween times Y3 and Y10 using the identical frequency (commonfrequency).

Signal processor 12501 performs the signal processing according to theMIMO transmission scheme, the space-time codes such as the space-timeblock code (however, the symbol mat be arranged on the frequency axis),and the MIMO transmission scheme in which the precoding is performed ornot performed, which are described in the first to twelfth exemplaryembodiments. Particularly, in the case that the precoding, the phasechange, and the power change are performed, signal processor 12501includes at least the sections in FIGS. 97 and 98 (or the sectionsexcept for the encoder in FIGS. 5 to 7 ).

Error-correction-coded data 11703, information signal 12204 associatedwith the modulation scheme, information signal 12205 of the parameterassociated with the modulation scheme, and information signal 12505associated with the transmission method are input to signal processor12501. In the case that information signal 12505 associated with thetransmission method is the information indicating that the precoding,the phase change, and the power change are performed, signal processor12501 performs the operation similar to that in FIGS. 97 and 98 (or thesections except for the encoder in FIGS. 5 to 7 ) of the first totwelfth exemplary embodiments. Accordingly, signal processor 12501outputs post-processing baseband signals 12502A and 12502B (it isassumed that signal processor 12501 performs the processing such as theinterleaving).

Post-processing baseband signal 12502A, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503Λ, and radio section 12503Λ outputstransmitted signal 12504A as the radio wave from antenna #1 (12505A)based on frame configuration signal 12210.

Post-processing baseband signal 12502B, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503B, and radio section 12503B outputstransmitted signal 12504B as the radio wave from antenna #2 (12505B)based on frame configuration signal 12210.

The configuration of the case that signal processor 12501 performs thetransmission method with the space-time block code will be describedbelow with reference to FIG. 128 .

Data signal (error-correction-coded data) 12801 and control signal 12806are input to mapper 12802, and mapper 12802 performs the mapping basedon the information about the modulation scheme included in controlsignal 12806, and outputs mapped signal 12803. For example, it isassumed that mapped signal 12803 is arranged in the order ofs0,s₁,s2,s3, . . . ,s(2i),s(2i+1), . . . (i is an integer of 0 or more).

Mapped signal 12803 and control signal 12806 are input to MISO (MultipleInput Multiple Output) processor 12804, and MISO processor 12804 outputspost-MISO-processing signals 12805A and 12805B in the case that controlsignal 12806 issues an instruction to transmit the signal using the MISO(Multiple Input Multiple Output) scheme. For example,post-MISO-processing signal 12805A is s0, s₁, s2, s3, . . . , s(2i),s(2i+1), . . . , and post-MISO-processing signal 12805B is −s1*,s0*−s3*, s2*, . . . , −s(2i+1)*, s(2i)*, . . . . The mark means acomplex conjugate.

At this point, post-MISO-processing signals 12805A and 12805B correspondto post-processing baseband signals 12502A and 12502B in FIG. 125 ,respectively. The space-time block coding method is not limited to theabove method.

Post-processing baseband signal 12502A, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503Λ, and radio section 12503Λ outputstransmitted signal 12504A as the radio wave from antenna #1 (12505A)based on frame configuration signal 12210.

Post-processing baseband signal 12502B, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503B, and radio section 12503B outputstransmitted signal 12504B as the radio wave from antenna #2 (12505B)based on frame configuration signal 12210.

FIG. 127 illustrates an example of the receiver that receives themodulated signal transmitted from the transmitter in FIG. 125 . In FIG.127 , the component similarly to that in FIG. 124 is designated by theidentical reference mark.

Quadrature baseband signal 11804 is input to synchronizer 12405, andsynchronizer 12405 performs the frequency synchronization, the timesynchronization, and the frame synchronization by detecting and usingpilot symbols 12601, 12604A, and 12604B in FIG. 126 , and outputssynchronization signal 12406.

Quadrature baseband signal 11804 and synchronization signal 12406 areinput to control information demodulator 12401, and control informationdemodulator 12401 demodulates control information symbols 12602, 12605A,and 1605B in FIG. 126 (and the error correction decoding), and outputscontrol information signal 12402.

Quadrature baseband signal 11804 and synchronization signal 12406 areinput to frequency offset and transmission path estimator 12403, andfrequency offset and transmission path estimator 12403 estimates afrequency offset and a transmission path variation caused by a currentusing pilot symbols 12601, 12604A, and 12604B in FIG. 126 , and outputsfrequency offset and transmission path variation estimated signal 12404.

Received signal 12702X received with antenna #1 (12701X) is input toradio section 12703X, and radio section 12703X performs the pieces ofprocessing such as the frequency conversion and the quadraturedemodulation (and the Fourier transform), and outputs quadraturebaseband signal 12704X.

Similarly, received signal 12702Y received with antenna #2 (12701Y) isinput to radio section 12703Y, and radio section 12703Y performs thepieces of processing such as the frequency conversion and the quadraturedemodulation (and the Fourier transform), and outputs quadraturebaseband signal 12704Y.

Quadrature baseband signals 12704X and 12704Y, control informationsignal 12402, frequency offset and transmission path variation estimatedsignal 12404, and synchronization signal 12406 are input to signalprocessor 12705. Signal processor 12705 determines the modulation schemeand the transmission method using control information signal 12402,performs the signal processing and the demodulation based on thedetermined modulation scheme and transmission method, obtains thelog-likelihood ratio of each bit in the data symbol, and outputslog-likelihood ratio signal 12706 (sometimes signal processor 12705performs the processing such as the deinterleaving).

Log-likelihood ratio signal 12706 and control information signal 12402are input to decoder 12707, and decoder 12707 performs the errorcorrection decoding from the error correction coding scheme included inthe control information, and outputs received data 12708.

Examples in which QAM of (Supplement 2), (Supplement 3), and (Supplement4) is used will be described below.

Example 1

It is assumed that the transmitter in FIG. 125 can transmit theplurality of block lengths (code lengths) as the error correction code.

For example, it is assumed that the transmitter in FIG. 125 selects oneof the error correction coding with the LDPC (block) code having theblock length (code length) of 16200 bits and the error correction codingwith the LDPC (block) code having the block length (code length) 64800bits to performs the error correction code. Accordingly, the followingtwo error correction schemes are considered.

<Error Correction Scheme #1>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 16200 bits (information:10800 bits and parity: 5400 bits).

<Error Correction Scheme #2>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 64800 bits (information:43200 bits and parity: 21600 bits).

It is assumed that 16QAM in FIG. 111 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets f=f_(#1) in FIG.111 using <error correction scheme #1>, and sets f=f_(#2) in FIG. 111using <error correction scheme #2>. At this point,

<Condition #H10>

In each transmission method corresponding to the configuration in FIG.125 ,

f_(#1)≠1 and f_(#2)≠1 and f_(#1)≠f_(#2) preferably hold. Therefore, thereceiver has a higher possibility of obtaining the high data receptionquality in both <error correction scheme #1> and <error correctionscheme #2> (because <error correction scheme #1> differs from <errorcorrection scheme #2> in a suitable value of f).

It is assumed that 64QAM in FIG. 112 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets g₁=g_(1,#1),g₂=g_(2,#1), and g₃=g_(3,#1) in FIG. 112 using <error correction scheme#1>, and sets g₁=g_(1,#2), g₂=g_(2,#2), and g₃=g_(3,#2) in FIG. 112using <error correction scheme #2>. Therefore, the following conditionpreferably holds.

<Condition #H11>

The following condition holds in each transmission method correspondingto the configuration in FIG. 125 .

{(g_(1,#1),g_(2,#1),g_(3,#1))+(1,3,5) and(g_(1,#1),g_(2,#1),g_(3,#1))≠(1,5,3) and(g_(1,#1),g_(2,#1),g_(3,#1))≠(3,1,5) and(g_(1,#1),g_(2,#1),g_(3,#1))≠(3,5,1) and(g_(1,#1),g_(2,#1),g_(3,#1))≠(5,1,3) and(g_(1,#1),g_(2,#1),g_(3,#1))≠(5,3,1)}

and

{(g_(1,#2),g_(2,#2),g_(3.#2))≠(1,3,5) and(g_(1,#2),g_(2,#2),g_(3.#2))≠(1,5,3) and(g_(1,#2),g_(2,#2),g_(3.#2))≠(3,1,5) and(g_(1,#2),g_(2.#2),g_(3.#2))≠(3,5,1) and(g_(1,#2),g_(2,#2),g_(3.#2))≠(5,1,3) and(g_(1,#2),g_(2,#2),g_(3,#2))≠(5,3,1)}

and

{{g_(1,#1)≠g_(1,#2) or g_(2,#1)≠g_(2,#2) or g_(3,#1)≠g_(3,#2)} holds}

hold.

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #1> and <errorcorrection scheme #2> (because <error correction scheme #1> differs from<error correction scheme #2> in a suitable set of g₁, g₂, and g₃).

It is assumed that 256QAM in FIG. 113 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1), andh₇=h_(7,#1) in FIG. 113 using <error correction scheme #1>, and setsh₁=h_(1,#2), h₂=h_(2,#2), h₃=h_(3,#2), h₄=h_(4,#2), h₅=h_(5,#2),h₆=h_(6,#2), and h₇=h_(7,#2) in FIG. 113 using <error correction scheme#2>. Therefore, the following condition preferably holds.

<Condition #H12>

The following condition holds in each transmission method correspondingto the configuration in FIG. 125 .

{When {a1 is an integer from 1 to 7 and a2 is an integer from 1 to 7 anda3 is an integer from 1 to 7 and a4 is an integer from 1 to 7 and a5 isan integer from 1 to 7 and a6 is an integer from 1 to 7 and a7 is aninteger from 1 to 7} and {x is an integer from 1 to 7 and y is aninteger from 1 to 7 and x≠y} and {ax≠ay holds for all values x and y}hold, (h_(a1,#1), h_(a2,#1), h_(a3,#1), h_(a4,#1), h_(a5,#1), h_(a6,#1),h_(a7,#1))≠(1,3,5,7,9,11,13) holds},and{when {a1 is an integer from 1 to 7 and a2 is an integer from 1 to 7 anda3 is an integer from 1 to 7 and a4 is an integer from 1 to 7 and a5 isan integer from 1 to 7 and a6 is an integer from 1 to 7 and a7 is aninteger from 1 to 7} and {x is an integer from 1 to 7 and y is aninteger from 1 to 7 and x≠y} and {ax≠ay holds for all values x and y}hold, (h_(a1,#2), h_(a2,#2), h_(a3,#2), h_(a4,#2), h_(a5,#2), h_(a6,#2),h_(a7,#2))+(1,3,5,7,9,11,13) holds}and{{h_(1,#1)≠h_(1,#2) or h_(2,#1)≠h_(2,#2) or h_(3,#1)≠h_(3,#2) orh_(4,#1)≠h_(4,#2) or h_(5,#1)≠h_(5,#2) or h_(6, #1)≠h_(6,#2) orh_(7,#1)+h₇,#2} holds.}hold.

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #1> and <errorcorrection scheme #2> (because <error correction scheme #1> differs from<error correction scheme #2> in a suitable set of h₁, h₂, h₃, h₄, h₅,h₆, and h₇).

The following is a summary of the above.

The following two error correction schemes are considered.

<Error Correction Scheme #1*>

The coding is performed using the block code having coding rate A andthe block length (code length) of B bits (A is a real number, 0<A<1holds, and B is an integer larger than 0).

<Error Correction Scheme #2*>

The coding is performed using the block code having coding rate A andthe block length (code length) of C bits (A is a real number, 0<A<1holds, C is an integer larger than 0, and B≠C holds).

It is assumed that 16QAM in FIG. 111 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets f=f_(#1) in FIG.111 using <error correction scheme #1*>, and sets f=f_(#2) in FIG. 111using <error correction scheme #2*>. At this point, <Condition #H10>preferably holds.

It is assumed that 64QAM in FIG. 112 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets g₁=g_(1,#1),g₂=g_(2,#1), and g₃=g_(3,#1) in FIG. 112 using <error correction scheme#1*>, and sets g₁=g_(1,#2), g₂=g_(2,#2), and g₃=g_(3,#2) in FIG. 112using <error correction scheme #2*>. At this point, <Condition #H11>preferably holds.

It is assumed that 256QAM in FIG. 113 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1), andh₇=h_(7,#1) in FIG. 113 using <error correction scheme #1*>, and setsh₁=h_(1,#2), h₂=h_(2,#2), h₃=h_(3,#2), h₄=h_(4,#2), h₅=h_(5,#2),h₆=h_(6,#2), and h₇=h_(7,#2) in FIG. 112 using <error correction scheme#2*>. At this point, <Condition #H12> preferably holds.

Example 2

It is assumed that the transmitter in FIG. 125 can transmit theplurality of block lengths (code lengths) as the error correction code.

For example, it is assumed that the transmitter in FIG. 125 selects oneof the error correction coding with the LDPC (block) code having theblock length (code length) of 16200 bits and the error correction codingwith the LDPC (block) code having the block length (code length) 64800bits to performs the error correction code. Accordingly, the followingtwo error correction schemes are considered.

<Error Correction Scheme #3>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 16200 bits (information:10800 bits and parity: 5400 bits).

<Error Correction Scheme #4>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 64800 bits (information:43200 bits and parity: 21600 bits).

It is assumed that 16QAM in FIG. 114 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets f₁=f_(1,#1) andf₂=f_(2,#1) in FIG. 114 using <error correction scheme #3>, and setsf₁=f_(1,#2) and f₂=f_(2,#2) in FIG. 114 using <error correction scheme#4>. At this point,

<Condition #H13>

The following condition holds in each transmission method correspondingto the configuration in FIG. 125 .

{f_(1,#1)≠f_(1,#2) or f_(2,#1)≠f_(2,#2)} preferably holds. Therefore,the receiver has a higher possibility of obtaining the high datareception quality in both <error correction scheme #3> and <errorcorrection scheme #4> (because <error correction scheme #3> differs from<error correction scheme #4> in a suitable set of f₁ and f₂).

It is assumed that 64QAM in FIG. 115 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets g₁=g_(1,#1),g₂=g_(2,#1), g₃=g_(3,#1), g₄=g_(4,#1), g₅=g_(5,#1), and g₆=g_(6,#1) inFIG. 115 using <error correction scheme #3>, and sets g₁=g₁,#2,g₂=g_(2,#2), g₃=g_(3,#2), g₄=g_(4,#2), g₅=g_(5,#2), and g₆=g_(6,#2) inFIG. 115 using <error correction scheme #4>. Therefore, the followingcondition preferably holds.

<Condition #H14>

The following condition holds in each transmission method correspondingto the configuration in FIG. 125 .

{{{g_(1,#1) ≠ g_(1,#2) and g_(1,#1) ≠ g_(2,#2) and g_(1,#1) ≠ g_(3,#2)}or {g_(2,#1) ≠ g_(1,#2) and g_(2,#1) ≠ g_(2,#2) and g_(2,#1) ≠ g_(3,#2)}or {g_(3,#1) ≠ g_(1,#2) and g_(3,#1) ≠ g_(2,#2) and g_(3,#1) ≠ g_(3,#2)}holds} or {{g_(4,#1) ≠ g_(4,#2) and g_(4,#1) ≠ g_(5,#2) and g_(4,#1) ≠g_(6,#2)} or {g_(5,#1) ≠ g_(4,#2) and g_(5,#1) ≠ g_(5,#2) and g_(5,#1) ≠g_(6,#2)} or {g_(6,#1) ≠ g_(4,#2) and g_(6,#1) ≠ g_(5,#2) and g_(6,#1) ≠g_(6,#2)} holds.} } holds.

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #3> and <errorcorrection scheme #4> (because <error correction scheme #3> differs from<error correction scheme #4> in a suitable set of g₁, g₂, g₃, g₄, g₅,and g₆).

It is assumed that 256QAM in FIG. 116 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1),h₇=h_(7,#1), h₈=h_(8,#1), h₉=h_(9,#1), h₁₀=h_(10,#1), h₁₁=h_(11,#1),h₁₂=h_(12,#1), h₁₃=h_(13,#1), and h₁₄=h_(14,#1) in FIG. 116 using <errorcorrection scheme #3>, and sets h₁=h_(1,#2), h₂=h_(2,#2), h₃=h_(3,#2),h₄=h_(4,#2), h₅=h_(5,#2), h₆=h_(6,#2), h₇=h_(7,#2), h₈=h_(8,#2),h₉=h_(9,#2), h₁₀=h_(10,#2), h₁₁=h_(11,#2), h₁₂=h_(12,#2), h₁₃=h_(13,#2),and h₁₄=h_(14,#2) in FIG. 116 using <error correction scheme #4>.Therefore, the following condition preferably holds.

<Condition #H15>

The following condition holds in each transmission method correspondingto the configuration in FIG. 125 .

{ {k is an integer from 1 to 7, and h_(1,#1) ≠ h_(k,#2) holds for allthe value of k} or {k is an integer from 1 to 7, and h_(2,#1) ≠ h_(k,#2)holds for all the value of k} or {k is an integer from 1 to 7, andh_(3,#1) ≠ h_(k,#2) holds for all the value of k} or {k is an integerfrom 1 to 7, and h_(4,#1) ≠ h_(k,#2) holds for all the value of k} or {kis an integer from 1 to 7, and h_(5,#1) ≠ h_(k,#2) holds for all thevalue of k} or {k is an integer from 1 to 7, and h_(6,#1) ≠ h_(k,#2)holds for all the value of k} or {k is an integer from 1 to 7, andh_(7,#1) ≠ h_(k,#2) holds for all the value of k} } or { {k is aninteger from 8 to 14, and h_(8,#1) ≠ h_(k,#2) holds for all the value ofk} or {k is an integer from 8 to 14, and h_(9,#1) ≠ h_(k,#2) holds forall the value of k} or {k is an integer from 8 to 14, and h_(10,#1) ≠h_(k,#2) holds for all the value of k} or {k is an integer from 8 to 14,and h_(11,#1) ≠ h_(k,#2) holds for all the value of k} or {k is aninteger from 8 to 14, and h_(12,#1) ≠ h_(k,#2) holds for all the valueof k} or {k is an integer from 8 to 14, and h_(13,#1) ≠ h_(k,#2) holdsfor all the value of k} or {k is an integer from 8 to 14, and _(h14,#1)≠ h_(k,#2) holds for all the value of k} }

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #3> and <errorcorrection scheme #4> (because <error correction scheme #3> differs from<error correction scheme #4> in a suitable set of h₁, h₂, h₃, h₄, h₅,h₆, h₇, h₈, h₉, h₁₀, h₁₁, h₁₂, h₁₃, and h₁₄).

The following is a summary of the above.

The following two error correction schemes are considered.

<Error Correction Scheme #3*>

The coding is performed using the block code having coding rate A andthe block length (code length) of B bits (A is a real number, 0<A<1holds, and B is an integer larger than 0).

<Error Correction Scheme #4*>

The coding is performed using the block code having coding rate A andthe block length (code length) of C bits (A is a real number, 0<A<1holds, C is an integer larger than 0, and B≠C holds).

It is assumed that 16QAM in FIG. 114 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets f₁=f_(1,#1) andf₂=f_(2,#1) in FIG. 114 using <error correction scheme #3*>, and setsf₁=f_(1,#2) and f₂=f_(2,#2) in FIG. 114 using <error correction scheme#4*>. At this point, <Condition #H13> preferably holds.

It is assumed that 64QAM in FIG. 115 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets g₁=g_(1,#1),g₂=g_(2,#1), g₃=g_(3,#1), g₄=g_(4,#1), g₅=g_(5,#1), and g₆=g_(6,#1) inFIG. 115 using <error correction scheme #3*>, and sets g₁=g_(1,#2),g₂=g_(2,#2), g₃=g_(3,#2), g₄=g_(4,#2), g₅=g_(5,#2), and g₆=g_(6,#2) inFIG. 115 using <error correction scheme #4*>. At this point, <Condition#H14> preferably holds.

It is assumed that 256QAM in FIG. 116 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1), andh₇=h_(7,#1) in FIG. 116 using <error correction scheme #3*>, and setsh₁=h_(1,#2), h₂=h_(2,#2), h₃=h_(3,#2), h₄=h_(4,#2), h₅=h_(5,#2),h₆=h_(6,#2), and h₇=h_(7,#2) in FIG. 116 using <error correction scheme#4*>. At this point, <Condition #H15> preferably holds.

Example 3

It is assumed that the transmitter in FIG. 125 can transmit theplurality of block lengths (code lengths) as the error correction code.

For example, it is assumed that the transmitter in FIG. 125 selects oneof the error correction coding with the LDPC (block) code having theblock length (code length) of 16200 bits and the error correction codingwith the LDPC (block) code having the block length (code length) 64800bits to performs the error correction code. Accordingly, the followingtwo error correction schemes are considered.

<Error Correction Scheme #5>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 16200 bits (information:10800 bits and parity: 5400 bits).

<Error Correction Scheme #6>

The coding is performed using the LDPC (block) code having the codingrate of ⅔ and the block length (code length) 64800 bits (information:43200 bits and parity: 21600 bits).

It is assumed that 16QAM in FIG. 119 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets k₁=k_(1,#1) andk₂=k_(2,#1) in FIG. 119 using <error correction scheme #5>, and setsk₁=k_(1,#2) and k₂=k_(2,#2) in FIG. 119 using <error correction scheme#6>. At this point,

<Condition #H16>

The following condition holds in each transmission method correspondingto the configuration in FIG. 125 .

{k_(1,#1)≠k_(1,#2) or k_(2,#1)≠k_(2,#2)} preferably holds. Therefore,the receiver has a higher possibility of obtaining the high datareception quality in both <error correction scheme #5> and <errorcorrection scheme #6> (because <error correction scheme #5> differs from<error correction scheme #6> in a suitable set of k₁ and k₂).

It is assumed that 64QAM in FIG. 120 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets m₁=m_(1,#1),m₂=m_(2,#1), m₃=m_(3,#1), m₄=m_(4,#1), m₅=m_(5,#1), m₆=m_(6,#1),m₇=m_(7,#1), and m₈=m_(8,#1) in FIG. 120 using <error correction scheme#5>, and sets m₁=m_(1,#2), m₂=m_(2,#2), m₃=m_(3,#2), m₄=m_(4,#2),m₅=m_(5,#2), m₆=m_(6,#2), m₇=m_(7,#2), and m₈=m_(8,#2) in FIG. 120 using<error correction scheme #6>. Therefore, the following conditionpreferably holds.

<Condition #H17>

The following condition holds in each transmission method correspondingto the configuration in FIG. 125 .

{ {{m_(1,#1) ≠ m_(1,#2) and m_(1,#1) ≠ m_(2,#2) and m_(1,#1) ≠ m_(3,#2)and m_(1,#1) ≠ m_(4,#2)} or {m_(2,#1) ≠ m_(1,#2) and m_(2,#1) ≠ m_(2,#2)and m_(2,#1) ≠ m_(3,#2) and m_(2,#1) ≠ m_(4,#2)} or {m_(3,#1) ≠ m_(1,#2)and m_(3,#1) ≠ m_(2,#2) and m_(3,#1) ≠ m_(3,#2) and m_(3,#1) ≠ m_(4,#2)}or {m_(4,#1) ≠ m_(1,#2) and m_(4,#1) ≠ m_(2,#2) and m_(4,#1) ≠ m_(3,#2)and m_(4,#1) ≠ m_(4,#2)} holds.} or {{m_(5,#1) ≠ m_(5,#2) and m_(5,#1) ≠m_(6,#2) and m_(5,#1) ≠ m_(7,#2) and m_(5,#1) ≠ m_(8,#2)} or {m_(6,#1) ≠m_(5,#2) and m_(6,#1) ≠ m_(6,#2) and m_(6,#1) ≠ m_(7,#2) and m_(6,#1) ≠m_(8,#2)} or {m_(7,#1) ≠ m_(5,#2) and m_(7,#1) ≠ m_(6,#2) and m_(7,#1) ≠m_(7,#2) and m_(7,#1) ≠ m_(8,#2)} or {m_(8,#1) ≠ m_(5,#2) and m_(8,#1) ≠m_(6,#2) and m_(8,#1) ≠ m_(7,#2) and m_(8,#1) ≠ m_(8,#2)} holds.} }holds.

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #5> and <errorcorrection scheme #6> (because <error correction scheme #5> differs from<error correction scheme #6> in a suitable set of m₁, m₂, m₃, m₄, m₅,m₆, m₇, and m₈).

It is assumed that 256QAM in FIG. 121 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets n₁=n_(1,#1),n₂=n_(2,#1), n₃=n_(3,#1), n₄=n_(4,#1), n₅=n_(5,#1), n₆=n_(6,#1),n₇=n_(7,#1), n₈=n_(8,#1), n₉=n_(9,#1), n₁₀=n_(10,#1), n₁₁=n_(11,#1),n₁₂=n_(12,#1), n₁₃=n_(13,#1), n₁₄=n_(14,#1), n₁₅=n_(15,#1), andn₁₆=n_(16,#1) in FIG. 121 using <error correction scheme #5>, and setsn₁=n_(1,#2), n₂=n_(2,#2), n₃=n_(3,#2), n₄=n_(4,#2), n₅=n_(5,#2),n₆=n_(6,#2), n₇=n_(7,#2), n₈=n_(8,#2), n₉=n_(9,#2), n₁₀=n_(10,#2),n₁₁=n_(11,#2), n₁₂=n_(12,#2), n₁₃=n_(13,#2), n₁₄=n_(14,#2),n₁₅=n_(15,#2), and n₁₆=n_(16,#2) in FIG. 121 using <error correctionscheme #6>. Therefore, the following condition preferably holds.

<Condition #H18>

The following condition holds in each transmission method correspondingto the configuration in FIG. 125 .

{ {k is an integer from 1 to 8, and n_(1,#1) ≠ n_(k,#2) holds for allthe value of k} or {k is an integer from 1 to 8, and n_(2,#1) ≠ n_(k,#2)holds for all the value of k} or {k is an integer from 1 to 8, andn_(3,#1) ≠ n_(k,#2) holds for all the value of k} or {k is an integerfrom 1 to 8, and n_(4,#1) ≠ n_(k,#2) holds for all the value of k} or {kis an integer from 1 to 8, and n_(5,#1) ≠ n_(k,#2) holds for all thevalue of k} or {k is an integer from 1 to 8, and n_(6,#1) ≠ n_(k,#2)holds for all the value of k} or {k is an integer from 1 to 8, andn_(7,#1) ≠ n_(k,#2) holds for all the value of k} or {k is an integerfrom 1 to 8, and n_(8,#1) ≠ n_(k,#2) holds for all the value of k} } or{ {k is an integer from 9 to 16, and n_(9,#1) ≠ n_(k,#2) holds for allthe value of k} or {k is an integer from 9 to 16, and n_(10,#1) ≠n_(k,#2) holds for all the value of k} or {k is an integer from 9 to 16,and n_(11,#1) ≠ n_(k,#2) holds for all the value of k} or {k is aninteger from 9 to 16, and n_(12,#1) ≠ n_(k,#2) holds for all the valueof k} or {k is an integer from 9 to 16, and n_(13,#1) ≠ n_(k,#2) holdsfor all the value of k} or {k is an integer from 9 to 16, and n_(14,#1)≠ n_(k,#2) holds for all the value of k} or {k is an integer from 9 to16, and n_(15,#1) ≠ n_(k,#2) holds for all the value of k} or {k is aninteger from 9 to 16, and n_(16,#1) ≠ n_(k,#2) holds for all the valueof k} }

Therefore, the receiver has a higher possibility of obtaining the highdata reception quality in both <error correction scheme #5> and <errorcorrection scheme #6> (because <error correction scheme #5> differs from<error correction scheme #6> in a suitable set of n₁, n₂, n₃, n₄, n₅,n₆, n₇, n₈, n₉, n₁₀, n₁₁, n₁₂, n₁₃, n₁₄, n₁₅, and n₁₆).

The following is a summary of the above.

The following two error correction schemes are considered.

<Error Correction Scheme #5*>

The coding is performed using the block code having coding rate A andthe block length (code length) of B bits (A is a real number, 0<A<1holds, and B is an integer larger than 0).

<Error Correction Scheme #6*>

The coding is performed using the block code having coding rate A andthe block length (code length) of C bits (A is a real number, 0<A<1holds, C is an integer larger than 0, and B≠C holds).

It is assumed that 16QAM in FIG. 119 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets k₁=k_(1,#1) andk₂=k_(2,#1) in FIG. 119 using <error correction scheme #5*>, and setsk₁=k_(1,#2) and k₂=k_(2,#2) in FIG. 119 using <error correction scheme#6*>. At this point, <Condition #H16> preferably holds.

It is assumed that 64QAM in FIG. 120 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets m₁=m_(1,#1),m₂=m_(2,#1), m₃=m_(3,#1), m₄=m_(4,#1), m₅=m_(5,#1), m₆=m_(6,#1),m₇=m_(7,#1), and m₈=m_(8,#1) in FIG. 120 using <error correction scheme#5*>, and sets m₁=m_(1,#2), m₂=m_(2,#2), m₃=m_(3,#2), m₄=m_(4,#2),m₅=m_(5,#2), m₆=m_(6,#2), m₇=m_(7,#2), and m₈=m_(8,#2) in FIG. 120 using<error correction scheme #6*>. At this point, <Condition #H17>preferably holds.

It is assumed that 256QAM in FIG. 121 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets n₁=n_(1,#1),n₂=n_(2,#1), n₃=n_(3,#1), n₄=n_(4,#1), n₅=n_(5,#1), n₆=n_(6,#1),n₇=n_(7,#1), n₈=n_(8,#1), n₉=n_(9,#1), n₁₀=n_(10,#1), n₁₁=n_(11,#1),n₁₂=n_(12,#1), n₁₃=n_(13,#1), n₁₄=n_(14,#1), n₁₅=n_(15,#1), andn₁₆=n_(16,#1) in FIG. 121 using <error correction scheme #5*>, and setsn₁=n_(1,#2), n₂=n_(2,#2), n₃=n_(3,#2), n₄=n_(4,#2), n₅=n_(5,#2),n₆=n_(6,#2), n₇=n_(7,#2), n₈=n_(8,#2), n₉=n_(9,#2), n₁₀=n_(10,#2),n₁₁=n_(11,#2), n₁₂=n_(12,#2), n₁₃=n_(13,#2), n₁₄=n_(14,#2),n₁₅=n_(15,#2), and n₁₆=n_(16,#2) in FIG. 121 using <error correctionscheme #6*>. At this point, <Condition #H18> preferably holds.

Although the detailed configuration is not illustrated in FIGS. 125 and127 , similarly the modulated signal can be transmitted and receivedusing the OFDM scheme and spectral spread communication scheme, whichare described in another exemplary embodiment.

Example 4

As described above with reference to FIG. 126 , sometimes thetransmitter in FIG. 125 performs the transmission method with thespace-time block code, when the one-stream signal is transmitted usingat least one antenna, or when the precoding, the phase change, and thepower change are performed. It is assumed that the transmitter in FIG.125 performs the following coding.

“The coding is performed using the block code having coding rate A andthe block length (code length) of B bits (A is a real number, 0<A<1holds, and B is an integer larger than 0).”

The following transmission methods are defined.

Transmission method #1: the one-stream signal is transmitted using atleast one antenna.

Transmission method #2: the precoding, the phase change, and the powerchange are performed.

Transmission method #3: the space-time block code is used.

It is assumed that 16QAM in FIG. 111 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets f=f_(#1) in FIG.111 when transmission method #X is adopted, and sets f=f_(#2) in FIG.111 when transmission method #Y is adopted. At this point,

<Condition #H19>

f_(#1)≠1 and f_(#2)+1 and f_(#1)≠f_(#2) preferably hold,

where (X,Y)=(1,2) or (1,3) or (2,3).

Therefore, the receiver has a high possibility of obtaining the highdata reception quality in both the adoption of transmission method #Xand the adoption of transmission method #Y (the adoption of transmissionmethod #X differs from the adoption of transmission method #Y in asuitable value of f).

It is assumed that 64QAM in FIG. 112 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets g₁=g_(1,#1),g₂=g_(2,#1), and g₃=g_(3,#1) in FIG. 112 when transmission method #X isadopted, and sets g₁=g_(1,#2), g₂=g_(2,#2), and g₃=g_(3,#2) in FIG. 112when transmission method #Y is adopted. Therefore, the followingcondition preferably holds.

<Condition #H20>

{(g_(1,#1),g_(2,#1),g_(3,#1))≠(1,3,5) and(g_(1,#1),g_(2,#1),g_(3.#1))≠(1,5,3) and(g_(1,#1),g_(2,#1),g_(3.#1))≠(3,1,5) and(g_(1,#1),g_(2.#1),g_(3.#1))≠(3,5,1) and(g_(1,#1),g_(2,#1),g_(3,#1))≠(5,1,3) and(g_(1,#1),g_(2,#1),g_(3,#1))≠(5,3,1)}

and

{(g_(1,#2),g_(2,#2),g_(3,#2))≠(1,3,5) and(g_(1,#2),g_(2,#2),g_(3.#2))≠(1,5,3) and(g_(1,#2),g_(2,#2),g_(3.#2))≠(3,1,5) and(g_(1,#2),g_(2.#2),g_(3.#2))≠(3,5,1) and(g_(1,#2),g_(2,#2),g_(3.#2))≠(5,1,3) and(g_(1,#2),g_(2,#2),g_(3,#2))≠(5,3,1)}

and

{{g_(1,#1)≠g_(1,#2) or g_(2,#1)≠g_(2,#2) or g_(3,#1)≠g_(3,#2)} holds.}

hold, where (X,Y)=(1,2) or (1,3) or (2,3).

Therefore, the receiver has a high possibility of obtaining the highdata reception quality in both the adoption of transmission method #Xand the adoption of transmission method #Y (the adoption of transmissionmethod #X differs from the adoption of transmission method #Y in asuitable set of g₁, g₂, and g₃).

It is assumed that 256QAM in FIG. 113 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1), andh₇=h_(7,#1) in FIG. 113 when transmission method #X is adopted, and setsh₁=h_(1,#2), h₂=h_(2,#2), h₃=h_(3,#2), h₄=h_(4,#2), h₅=h_(5,#2),h₆=h_(6,#2), and h₇=h_(7,#2) in FIG. 113 when transmission method #Y isadopted. Therefore, the following condition preferably holds.

<Condition #H21>

{When {a1 is an integer from 1 to 7 and a2 is an integer from 1 to 7 anda3 is an integer from 1 to 7 and a4 is an integer from 1 to 7 and a5 isan integer from 1 to 7 and a6 is an integer from 1 to 7 and a7 is aninteger from 1 to 7} and {x is an integer from 1 to 7 and y is aninteger from 1 to 7 and x≠y} and {ax≠ay holds for all values x and y}hold,(h_(a1,#1),h_(a2,#1),h_(a3,#1),h_(a4,#1),h_(a5,#1),h_(a6,#1),h_(a7,#1))≠(1,3,5,7,9,11,13)holds.},and{when {a1 is an integer from 1 to 7 and a2 is an integer from 1 to 7 anda3 is an integer from 1 to 7 and a4 is an integer from 1 to 7 and a5 isan integer from 1 to 7 and a6 is an integer from 1 to 7 and a7 is aninteger from 1 to 7} and {x is an integer from 1 to 7 and y is aninteger from 1 to 7 and x≠y} and {ax≠ay holds for all values x and y}hold,(h_(a1,#2),h_(a2,#2),h_(a3,#2),h_(a4,#2),h_(a5,#2),h_(a6,#2),h_(a7,#2))≠(1,3,5,7,9,11,13)holds.}and{{h_(1,#1)≠h_(1,#2) or h_(2,#1)≠h_(2,#2) or h_(3,#1)≠h_(3,#2) orh_(4,#1)≠h_(4,#2) or h_(5,#1)≠h_(5,#2) or h_(6,#1)≠h_(6,#2) orh_(7,#1)≠h_(7,#2)} holds.}hold, where (X,Y)=(1,2) or (1,3) or (2,3).

Therefore, the receiver has a high possibility of obtaining the highdata reception quality in both the adoption of transmission method #Xand the adoption of transmission method #Y (the adoption of transmissionmethod #X differs from the adoption of transmission method #Y in asuitable set of h₁, h₂, h₃, h₄, h₅, h₆, and h₇).

Example 5

As described above with reference to FIG. 126 , sometimes thetransmitter in FIG. 125 performs the transmission method with thespace-time block code, when the one-stream signal is transmitted usingat least one antenna, or when the precoding, the phase change, and thepower change are performed. It is assumed that the transmitter in FIG.125 performs the following coding.

“The coding is performed using the block code having coding rate A andthe block length (code length) of B bits (A is a real number, 0<A<1holds, and B is an integer larger than 0).”

The following transmission methods are defined.

Transmission method #1: the one-stream signal is transmitted using atleast one antenna.

Transmission method #2: the precoding, the phase change, and the powerchange are performed.

Transmission method #3: the space-time block code is used.

It is assumed that 16QAM in FIG. 114 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets f₁=f_(1,#1) andf₂=f_(2,#1) in FIG. 114 when transmission method #X is adopted, and setsf₁=f_(1,#2) and f₂=f_(2,#2) in FIG. 114 when transmission method #Y isadopted. At this point,

<Condition #H22>

{f_(1,#1)≠f_(1,#2) or f_(2,#1)≠f_(2,#2)} preferably holds, where(X,Y)=(1,2) or (1,3) or (2,3).

Therefore, the receiver has a high possibility of obtaining the highdata reception quality in both the adoption of transmission method #Xand the adoption of transmission method #Y (the adoption of transmissionmethod #X differs from the adoption of transmission method #Y in asuitable set of f₁ and f₂).

It is assumed that 64QAM in FIG. 115 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets g₁=g_(1,#1),g₂=g_(2,#1), g₃=g_(3,#1), g₄=g_(4,#1), g₅=g_(5,#1), and g₆=g_(6,#1) inFIG. 115 when transmission method #X is adopted, and sets g₁=g_(1,#2),g₂=g_(2,#2), g₃=g_(3,#2), g₄=g_(4,#2), g₅=g_(5,#2), and g₆=g_(6,#2) inFIG. 115 when transmission method #Y is adopted. Therefore, thefollowing condition preferably holds.

<Condition #H23>

{ {{g_(1,#1) ≠ g_(1,#2) and g_(1,#1) ≠ g_(2,#2) and g_(1,#1) ≠ g_(3,#2)}or {g_(2,#1) ≠ g_(1,#2) and g_(2,#1) ≠ g_(2,#2) and g_(2,#1) ≠ g_(3,#2)}or {g_(3,#1) ≠ g_(1,#2) and g_(3,#1) ≠ g_(2,#2) and g_(3,#1) ≠ g_(3,#2)}holds.} or {{g_(4,#1) ≠ g_(4,#2) and g_(4,#1) ≠ g_(5,#2) and g_(4,#1) ≠g_(6,#2)} or {g_(5,#1) ≠ g_(4,#2) and g_(5,#1) ≠ g_(5,#2) and g_(5,#1) ≠g_(6,#2)} or {g_(6,#1) ≠ g_(4,#2) and g_(6,#1) ≠ g_(5,#2) and g_(6,#1) ≠g_(6,#2)} holds. } holds, where (X,Y) = (1,2) or (1,3) or (2,3).

Therefore, the receiver has a high possibility of obtaining the highdata reception quality in both the adoption of transmission method #Xand the adoption of transmission method #Y (the adoption of transmissionmethod #X differs from the adoption of transmission method #Y in asuitable set of g₁, g₂, g₃, g₄, g₅, and g₆).

It is assumed that 256QAM in FIG. 116 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets h₁=h_(1,#1),h₂=h_(2,#1), h₃=h_(3,#1), h₄=h_(4,#1), h₅=h_(5,#1), h₆=h_(6,#1),h₇=h_(7,#1), h₈=h_(8,#1), h₉=h_(9,#1), h₁₀=h_(10,#1), h₁₁=h_(11,#1),h₁₂=h_(12,#1), h₁₃=h_(13,#1), and h₁₄=h_(14,#1) in FIG. 116 whentransmission method #X is adopted, and sets h₁=h_(1,#2), h₂=h_(2,#2),h₃=h_(3,#2), h₄=h_(4,#2), h₅=h_(5,#2), h₆=h_(6,#2), h₇=h_(7,#2),h₈=h_(8,#2), h₉=h_(9,#2), h₁₀=h_(10,#2), h₁₁=h_(11,#2), h₁₂=h_(12,#2),h₁₃=h_(13,#2), and h₁₄=h_(14,#2) in FIG. 116 when transmission method #Yis adopted. Therefore, the following condition preferably holds.

<Condition #H24>

{ {k is an integer from 1 to 7, and h_(1,#1) ≠ h_(k,#2) holds for allthe value of k} or {k is an integer from 1 to 7, and h_(2,#1) ≠ h_(k,#2)holds for all the value of k} or {k is an integer from 1 to 7, andh_(3,#1) ≠ h_(k,#2) holds for all the value of k} or {k is an integerfrom 1 to 7, and h_(4,#1) ≠ h_(k,#2) holds for all the value of k} or {kis an integer from 1 to 7, and h_(5,#1) ≠ h_(k,#2) holds for all thevalue of k} or {k is an integer from 1 to 7, and h_(6,#1) ≠ h_(k,#2)holds for all the value of k} or {k is an integer from 1 to 7, andh_(7,#1) ≠ h_(k,#2) holds for all the value of k} } or { {k is aninteger from 8 to 14, and h_(8,#1) ≠ h_(k,#2) holds for all the value ofk} or {k is an integer from 8 to 14, and h_(9,#1) ≠ h_(k,#2) holds forall the value of k} or {k is an integer from 8 to 14, and h_(10,#1) ≠h_(k,#2) holds for all the value of k} or {k is an integer from 8 to 14,and h_(11,#1) ≠ h_(k,#2) holds for all the value of k} or {k is aninteger from 8 to 14, and h_(12,#1) ≠ h_(k,#2) holds for all the valueof k} or {k is an integer from 8 to 14, and h_(13,#1) ≠ h_(k,#2) holdsfor all the value of k} or {k is an integer from 8 to 14, and _(h14,#1)≠ h_(k,#2) holds for all the value of k} } where (X,Y) = (1,2) or (1,3)or (2,3).

Therefore, the receiver has a high possibility of obtaining the highdata reception quality in both the adoption of transmission method #Xand the adoption of transmission method #Y (the adoption of transmissionmethod #X differs from the adoption of transmission method #Y in asuitable set of h₁, h₂, h₃, h₄, h₅, h₆, h₇, h₈, h₉, h₁₀, h₁₁, h₁₂, h₁₃,and h₁₄).

Example 6

As described above with reference to FIG. 126 , sometimes thetransmitter in FIG. 125 performs the transmission method with thespace-time block code, when the one-stream signal is transmitted usingat least one antenna, or when the precoding, the phase change, and thepower change are performed. It is assumed that the transmitter in FIG.125 performs the following coding.

“The coding is performed using the block code having coding rate A andthe block length (code length) of B bits (A is a real number, 0<A<1holds, and B is an integer larger than 0).”

The following transmission methods are defined.

Transmission method #1: the one-stream signal is transmitted using atleast one antenna.

Transmission method #2: the precoding, the phase change, and the powerchange are performed.

Transmission method #3: the space-time block code is used.

It is assumed that 16QAM in FIG. 119 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets k₁=k_(1,#1) andk₂=k_(2,#1) in FIG. 119 when transmission method #X is adopted, and setsk₁=k_(1,#2) and k₂=k_(2,#2) in FIG. 119 when transmission method #Y isadopted. At this point,

<Condition #H25>

{k_(1,#1)≠k_(1,#2) or k_(2,#1)+k_(2,#2)} preferably holds, where(X,Y)=(1,2) or (1,3) or (2,3).

Therefore, the receiver has a high possibility of obtaining the highdata reception quality in both the adoption of transmission method #Xand the adoption of transmission method #Y (the adoption of transmissionmethod #X differs from the adoption of transmission method #Y in asuitable set of k₁ and k₂).

It is assumed that 64QAM in FIG. 120 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets m₁=m_(1,#1),m₂=m_(2,#1), m₃=m_(3,#1), m₄=m_(4,#1), m₅=m_(5,#1), m₆=m_(6,#1),m₇=m_(7,#1), and m₈=m_(8,#1) in FIG. 120 when transmission method #X isadopted, and sets m₁=m_(1,#2), m₂=m_(2,#2), m₃=m_(3,#2), m₄=m_(4,#2),m₅=m_(5,#2), m₆=m_(6,#2), m₇=m_(7,#2), and m₈=m_(8,#2) in FIG. 120 whentransmission method #Y is adopted. Therefore, the following conditionpreferably holds.

<Condition #H26>

{ {{m_(1,#1) ≠ m_(1,#2) and m_(1,#1) ≠ m_(2,#2) and m_(1,#1) ≠ m_(3,#2)and m_(1,#1) ≠ m_(4,#2)} or {m_(2,#1) ≠ m_(1,#2) and m_(2,#1) ≠ m_(2,#2)and m_(2,#1) ≠ m_(3,#2) and m_(2,#1) ≠ m_(4,#2)} or {m_(3,#1) ≠ m_(1,#2)and m_(3,#1) ≠ m_(2,#2) and m_(3,#1) ≠ m_(3,#2) and m_(3,#1) ≠ m_(4,#2)}or {m_(4,#1) ≠ m_(1,#2) and m_(4,#1) ≠ m_(2,#2) and m_(4,#1) ≠ m_(3,#2)and m_(4,#1) ≠ m_(4,#2)} holds.} or {{m_(5,#1) ≠ m_(5,#2) and m_(5,#1) ≠m_(6,#2) and m_(5,#1) ≠ m_(7,#2) and m_(5,#1) ≠ m_(8,#2)} or {m_(6,#1) ≠m_(5,#2) and m_(6,#1) ≠ m_(6,#2) and m_(6,#1) ≠ m_(7,#2) and m_(6,#1) ≠m_(8,#2)} or {m_(7,#1) ≠ m_(5,#2) and m_(7,#1) ≠ m_(6,#2) and m_(7,#1) ≠m_(7,#2) and m_(7,#1) ≠ m_(8,#2)} or {m_(8,#1) ≠ m_(5,#2) and m_(8,#1) ≠m_(6,#2) and m_(8,#1) ≠ m_(7,#2) and m_(8,#1) ≠ m_(8,#2)} holds.} }holds, where (X,Y) = (1,2) or (1,3) or (2,3).

Therefore, the receiver has a high possibility of obtaining the highdata reception quality in both the adoption of transmission method #Xand the adoption of transmission method #Y (the adoption of transmissionmethod #X differs from the adoption of transmission method #Y in asuitable set of m₁, m₂, m₃, m₄, m₅, m₆, m₇, and m₈).

It is assumed that 256QAM in FIG. 121 is used in the transmitter in FIG.125 . At this point, the transmitter in FIG. 125 sets n₁=n_(1,#1),n₂=n_(2,#1), n₃=n_(3,#1), n₄=n_(4,#1), n₅=n_(5,#1), n₆=n_(6,#1),n₇=n_(7,#1), n₈=n_(8,#1), n₉=n_(9,#1), n₁₀=n_(10,#1), n₁₁=n_(11,#1),n₁₂=n_(12,#1), n₁₃=n_(13,#1), n₁₄=n_(14,#1), n₁₅=n_(15,#1), andn₁₆=n_(16,#1) in FIG. 121 when transmission method #X is adopted, andsets n₁=n_(1,#2), n₂=n_(2,#2), n₃=n_(3,#2), n₄=n_(4,#2), n₅=n_(5,#2),n₆=n_(6,#2), n₇=n_(7,#2), n₈=n_(8,#2), n₉=n_(9,#2), n₁₀=n_(10,#2),n₁₁=n_(11,#2), n₁₂=n_(12,#2), n₁₃=n_(13,#2), n₁₄=n_(14,#2),n₁₅=n_(15,#2), and n₁₆=n_(16,#2) in FIG. 121 when transmission method #Yis adopted. Therefore, the following condition preferably holds.

<Condition #H27>

{ {k is an integer from 1 to 8, and n_(1,#1) ≠ n_(k,#2) holds for allthe value of k} or {k is an integer from 1 to 8, and n_(2,#1) ≠ n_(k,#2)holds for all the value of k} or {k is an integer from 1 to 8, andn_(3,#1) ≠ n_(k,#2) holds for all the value of k} or {k is an integerfrom 1 to 8, and n_(4,#1) ≠ n_(k,#2) holds for all the value of k} or {kis an integer from 1 to 8, and n_(5,#1) ≠ n_(k,#2) holds for all thevalue of k} or {k is an integer from 1 to 8, and n_(6,#1) ≠ n_(k,#2)holds for all the value of k} or {k is an integer from 1 to 8, andn_(7,#1) ≠ n_(k,#2) holds for all the value of k} or {k is an integerfrom 1 to 8, and n_(8,#1) ≠ n_(k,#2) holds for all the value of k} } or{ {k is an integer from 9 to 16, and n_(9,#1) ≠ n_(k,#2) holds for allthe value of k} or {k is an integer from 9 to 16, and n_(10,#1) ≠n_(k,#2) holds for all the value of k} or {k is an integer from 9 to 16,and n_(11,#1) ≠ n_(k,#2) holds for all the value of k} or {k is aninteger from 9 to 16, and n_(12,#1) ≠ n_(k,#2) holds for all the valueof k} or {k is an integer from 9 to 16, and n_(13,#1) ≠ n_(k,#2) holdsfor all the value of k} or {k is an integer from 9 to 16, and n_(14,#1)≠ n_(k,#2) holds for all the value of k} or {k is an integer from 9 to16, and n_(15,#1) ≠ n_(k,#2) holds for all the value of k} or {k is aninteger from 9 to 16, and n_(16,#1) ≠ n_(k,#2) holds for all the valueof k} } , where (X,Y) = (1,2) or (1,3) or (2,3).

Therefore, the receiver has a high possibility of obtaining the highdata reception quality in both the adoption of transmission method #Xand the adoption of transmission method #Y (the adoption of transmissionmethod #X differs from the adoption of transmission method #Y in asuitable set of n₁, n₂, n₃, n₄, n₅, n₆, n₇, n₈, n₉, n₁₀, n₁₁, n₁₂, n₁₃,n₁₄, n₁₅, and n₁₆).

Although the detailed configuration is not illustrated in FIGS. 125 and127 , similarly the modulated signal can be transmitted and receivedusing the OFDM scheme and spectral spread communication scheme, whichare described in another exemplary embodiment.

As described above, when the transmitter performs the modulation(mapping) to transmit the modulated signal, the transmitter transmitsthe control information such that the receiver can identify themodulation scheme and the parameters of the modulation scheme, whichallows the receiver in FIG. 127 to perform signal detection and thedemapping (demodulation) by obtaining the control information.

(Supplement 7)

The plurality of exemplary embodiments and supplements may be combined.

The contents of the exemplary embodiments and supplements are describedonly by way of example. For example, even if “the modulation scheme, theerror correction coding scheme (such as the error correction code, codelength, and coding rate, which should be used), and the controlinformation” are illustrated, the contents can be performed by thesimilar configuration in the case that “another modulation scheme,another error correction coding scheme (such as the error correctioncode, code length, and coding rate, which should be used), and anothercontrol information” are applied.

The contents of the exemplary embodiments and supplements can beperformed even if a modulation scheme except for the modulation schemeof the present disclosure modulation scheme is used. For example, APSK(Amplitude Phase Shift Keying) (such as 16APSK, 64APSK, 128APSK,256APSK, 1024APSK, and 4096APSK), PAM (Pulse Amplitude Modulation) (suchas 4PAM, 8PAM, 16PAM, 64PAM, 128PAM, 256PAM, 1024PAM, and 4096PAM), PSK(Phase Shift Keying) (such as BPSK, QPSK, 8PSK, 16PSK, 64PSK, 128PSK,256PSK, 1024PSK, and 4096PSK), QAM (Quadrature Amplitude Modulation)(such as 4QAM, 8QAM, 16QAM, 64QAM, 128QAM, 256QAM, 1024QAM, and 4096QAM)may be applied, or uniform mapping and nonuniform modulation scheme maybe performed.

The method for arranging the 2, 4, 8, 16, 64, 128, 256, or 1024 signalpoints in the I-Q plane (the modulation scheme having the 2, 4, 8, 16,64, 128, 256, or 1024 signal points) may be switched by the time, thefrequency, or the time and frequency.

The configuration (for example, FIGS. 5, 6, 7, 97, and 98 ) thatperforms the pieces of processing such as the precoding (weightingsynthesis), the phase change, and the power change on modulated signals1 pursuant to the first modulation scheme and modulated signal s2pursuant to the second modulation scheme are described above. Eachexemplary embodiment may be implemented by performing the followingprocessing instead of the above pieces of processing.

The processing method will be described below.

FIGS. 129 and 130 illustrate modifications of “the configuration (forexample, FIGS. 5, 6, 7, 97, and 98 ) that performs the pieces ofprocessing such as the precoding (weighting synthesis), the phasechange, and the power change on modulated signal s1 pursuant to thefirst modulation scheme and modulated signal s2 pursuant to the secondmodulation scheme”.

In the configuration of FIGS. 129 and 130 , a phase changer is added toa front stage of weighting synthesis (precoding). The component similarto that in FIGS. 5, 6, and 7 is designated by the identical referencemark, and the detailed description is omitted.

Phase changer 12902 in FIG. 129 performs first phase change processingon modulated signal 12901 output from mapper 504 such that a phase ofmodulated signal 12901 differs from that of modulated signal 505A, andoutputs phase-changed modulated signal s₂(t) (505B) to power changer506B.

Phase changer 13002 in FIG. 130 performs first phase change processingon modulated signal 13001 output from mapper 504 such that a phase ofmodulated signal 13001 differs from that of modulated signal 505A, andoutputs phase-changed modulated signal s₂(t) (505B) to power changer506B.

FIG. 131 illustrates a modification of the configuration example of thetransmitter in FIG. 129 . FIG. 132 illustrates a modification of theconfiguration example of the transmitter in FIG. 130 .

Phase changer 13102 in FIG. 131 performs second phase change processingon modulated signal 13101 output from mapper 504, and outputsphase-changed modulated signal s1 (t) (505A) to power changer 506A.

Phase changer 13202 in FIG. 132 performs second phase change processingon modulated signal 13201 output from mapper 504, and outputsphase-changed modulated signal s1 (t) (505A) to power changer 506A.

As illustrated in FIGS. 131 and 132 , the phase change may be performedon not only one of the modulated signals output from the mapper but alsoboth the modulated signals.

The phase change processing of phase changers (12902, 13002, 13102, and13202) can be given by the following numerical expression.

[Mathematical  formula  374] $\begin{pmatrix}I^{\prime} \\Q^{\prime}\end{pmatrix} = {\begin{pmatrix}{\cos\left( {\lambda(i)} \right)} & {- {\sin\left( {\lambda(i)} \right)}} \\{\sin\left( {\lambda(i)} \right)} & {\cos\left( {\lambda(i)} \right)}\end{pmatrix}\begin{pmatrix}I \\Q\end{pmatrix}}$

In the formula, λ(i) is a phase, λ(i) is a function of i (for example,the time, the frequency, and the slot), I and Q are an in-phasecomponent of the input signal and a quadrature component, and phasechangers (12902, 13002, 13102, and 13202) output I′ and Q′.

The receiver that receives the modulated signal transmitted using theconfigurations in FIGS. 129 to 132 performs the signal processingcorresponding to the above signal processing, and obtains thelog-likelihood ratio of each bit included in the modulated signal.

The method for arranging the 2, 4, 8, 16, 64, 128, 256, or 1024 signalpoints in the I-Q plane (the modulation scheme having the 2, 4, 8, 16,64, 128, 256, or 1024 signal points) is not limited to the signal pointarranging method of the above modulation schemes. Accordingly, themapper has the function of outputting the in-phase component and thequadrature component based on the plurality of bits, and then performingthe precoding and the phase change becomes effective function of thepresent disclosure.

In the twelfth exemplary embodiments, the precoding weight and the phaseare changed on the time axis. However, as described above, the twelfthexemplary embodiment can be implemented even if the multi-carriertransmission scheme such as the OFDM transmission is used. Particularly,when the precoding switching method is changed only by the number oftransmitted signals, the receiver can recognize the method for switchingthe precoding weight and the phase by obtaining the information aboutthe number of transmitted signals transmitted from the transmitter.

In the description, for example, it is conceivable that communicationand broadcasting equipment such as a broadcasting station, a basestation, an access point, a terminal, and a mobilephone includes thetransmitter, and it is conceivable that communication equipment such asa television set, a radio receiver, a terminal, a personal computer, amobilephone, an access point, and a base station includes the receiver.The transmitter and receiver of the present disclosure are equipmenthaving a communication function, and it is conceivable that theequipment can be connected to a device, such as a television set, aradio receiver, a terminal, a personal computer, and a mobilephone,which executes an application, through a certain interface.

In the twelfth exemplary embodiments, the symbols, such as the pilotsymbol (for example, a preamble, a unique word, a post-amble, and areference symbol) and the control information symbol, which excludes thedata symbol, may be arranged in the frame in any way. Although the termsof the pilot symbol and control information symbol are used, any way ofcalling may be used and the function itself is required.

For example, the pilot symbol may be a known symbol modulated using thePSK modulation in the transmitter and receiver (or the receiver mayrecognize the symbol transmitted from the transmitter by synchronizingwith the transmitter), and the receiver performs the frequencysynchronization, the time synchronization, the channel estimation (ofeach modulated signal) (estimation of CSI (Channel State Information)),and the signal detection using the pilot symbol.

The control information symbol is used to transmit the information (forexample, the coding rates of the modulation scheme, error correctioncoding scheme, and error correction coding scheme, which are used in thecommunication, and setting information in an upper layer) necessary tobe transmitted to the communication partner in order to conductcommunication except for the data (of the application).

The present disclosure is not limited to each exemplary embodiment, andvarious changes can be made. For example, each exemplary embodiment isimplemented as the communication device. Alternatively, thecommunication method used in the communication device may be performedas software.

The precoding switching method in the method for transmitting the twomodulated signals from the two antennas is described above.Alternatively, a method for performing the precoding on four mappedsignals, generating four modulated signals, and transmitting the fourmodulated signals from four antennas, namely, a method for performingthe precoding on N mapped signals, generating N modulated signals, andtransmitting the N modulated signals from N antennas can similarly beperformed as the precoding switching method for changing the precodingweight (matrix).

In the description, the terms of the precoding and the precoding weightare used. However, in the present disclosure, any way of calling may beused and the function itself is required.

Different pieces of data may be transmitted using streams s1(t) ands2(t), or identical data may be transmitted using streams s1(t) ands2(t).

Although one transmitting antenna for the transmitter and one receivingantenna for the receiver are illustrated in the drawings, thetransmitter and receiver may be constructed with a plurality ofantennas.

There is a frame transmitted from the transmitter, which is omitteddepending on the exemplary embodiment in which it is necessary to notifythe transmitter and receiver of the transmission method (MIMO, SISO, thespace-time block code, the interleaving scheme), the modulation scheme,and the error correction coding scheme. The receiver changes theoperation by obtaining the frame.

The bit length adjusting method is described in the first to eleventhexemplary embodiments, and the case that the bit length adjustingmethods of the first to eleventh exemplary embodiments are applied tothe DVB standard is described in the twelfth exemplary embodiment. Inthe first to twelfth exemplary embodiments, the bit length adjustingmethod in the transmitter is described with reference to FIGS. 57, 60,73, 78, 79, 80, 83, 91, and 93 , and the operation of the receiver isdescribed with reference to FIGS. 85, 87, 88, and 96 . In the first totwelfth exemplary embodiments, the MIMO transmission method (theprecoding (weighting synthesis), the power change, and the phase changeare used) is described with reference to FIGS. 5, 6, 7, 97, and 98 .

At this point, the first to twelfth exemplary embodiments can beimplemented, even if the space-time block code and the space-frequencyblock code (symbols are arranged in the frequency direction) in FIG. 128(sometimes referred to as MISO transmission scheme or transmissiondiversity) is used instead of the MIMO transmission method (precoding(weighting synthesis), the power change, and the phase change are used)in FIGS. 5, 6, 7, 97, and 98 as the transmission method after the bitlength adjustments of the first to twelfth exemplary embodiments. Thatis, the bit series (digital signal) in which the bit length is adjustedusing the configurations in FIGS. 57, 60, 73, 78, 79, 80, 83, 91, and 93corresponds to data signal 12801 in FIG. 128 , and then the mapping andthe MISO processing are performed as illustrated in FIG. 128 .

The method of the space-time block code and the space-frequency blockcode (symbols are arranged in the frequency direction) (sometimesreferred to as MISO transmission scheme or transmission diversity) isnot limited to the configuration in FIG. 128 , but the space-time blockcode and the space-frequency block code may be transmitted asillustrated in FIG. 133 . The configuration in FIG. 133 will bedescribed below (in FIG. 133 , the component similar to that in FIG. 128is designated by the identical reference mark).

Data signal (error-correction-coded data) 12801 and control signal 12806are input to mapper 12802, and mapper 12802 performs the mapping basedon the information about the modulation scheme included in controlsignal 12806, and outputs mapped signal 12803. For example, it isassumed that mapped signal 12803 is arranged in the order ofs0,s1,s2,s3, . . . ,s(2i),s(2i+1), . . . (i is an integer of 0 or more).

Mapped signal 12803 and control signal 12806 are input to MISO (MultipleInput Multiple Output) processor 12804, and MISO processor 12804 outputspost-MISO-processing signals 12805A and 12805B in the case that controlsignal 12806 issues an instruction to transmit the signal using the MISO(Multiple Input Multiple Output) scheme. For example,post-MISO-processing signal 12805A is s0, −s1*, s2, −s3*, . . . , s(2i),−s(2i+1)*, . . . , and post-MISO-processing signal 12805B is s1, s0*s3,s2*, . . . , s(2i+1), s(2i)*, . . . . The mark means a complexconjugate.

At this point, post-MISO-processing signals 12805A and 12805B correspondto post-processing baseband signals 12502A and 12502B in FIG. 125 ,respectively. The space-time block coding method is not limited to theabove method. Post-processing baseband signal 12502A, control symbolsignal 12208, pilot symbol signal 12209, and frame configuration signal12210 are input to radio section 12503Λ, and radio section 12503Λoutputs transmitted signal 12504A as the radio wave from antenna #1(12505A) based on frame configuration signal 12210.

Post-processing baseband signal 12502B, control symbol signal 12208,pilot symbol signal 12209, and frame configuration signal 12210 areinput to radio section 12503B, and radio section 12503B outputstransmitted signal 12504B as the radio wave from antenna #2 (12505B)based on frame configuration signal 12210.

The bit length adjusting method is described in the first to eleventhexemplary embodiments, and the case that the bit length adjustingmethods of the first to eleventh exemplary embodiments are applied tothe DVB standard is described in the twelfth exemplary embodiment. Inthe first to twelfth exemplary embodiments, the bit length adjustingmethod in the transmitter is described with reference to FIGS. 57, 60,73, 78, 79, 80, 83, 91, and 93 , and the operation of the receiver isdescribed with reference to FIGS. 85, 87, 88, and 96 . In the first totwelfth exemplary embodiments, the MIMO transmission method (theprecoding (weighting synthesis), the power change, and the phase changeare used) is described with reference to FIGS. 5, 6, 7, 97, and 98 .

At this point, the first to twelfth exemplary embodiments can beimplemented, even if the single-stream transmission is performed insteadof the MIMO transmission method (precoding (weighting synthesis), thepower change, and the phase change are used) in FIGS. 5, 6, 7, 97, and98 as the transmission method after the bit length adjustments of thefirst to twelfth exemplary embodiments.

That is, the bit series (digital signal) in which the bit length isadjusted using the configurations in FIGS. 57, 60, 73, 78, 79, 80, 83,91, and 93 corresponds to bit series 503 in FIGS. 5, 6, and 7 or bitseries 9701 in FIGS. 97 and 98 , and is input to mapper 504 in FIGS. 5,6, and 7 or mapper 9702 in FIGS. 97 and 98 .

Modulation scheme α of s₁(t) is used to transmit the x-bit data, but thedata is not transmitted in s2(t) (non-modulation, data transmission ofy=0 bit). Accordingly, (x+y=x+0=x) is obtained. For (x+y=x+0=x), thefirst to twelfth exemplary embodiments can also be implemented in thecase that the single stream is transmitted.

(Supplement 8)

Matrix F for the weighting synthesis (precoding) is indicated in thedescription. Alternatively, each exemplary embodiment of the presentdisclosure can be implemented even if the following precoding matrix F(or F(i)) is used.

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 375} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 10} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 376} \right\rbrack & \; \\{{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\; 0}} \\{\alpha \times e^{j\; 0}} & e^{j\;\pi}\end{pmatrix}}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 11} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 377} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}} \\{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 12} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 378} \right\rbrack & \; \\{{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\; 0} & {\alpha \times e^{j\;\pi}} \\{\alpha \times e^{j\; 0}} & e^{j\; 0}\end{pmatrix}}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 13} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 379} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\;\pi}} \\{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\; 0}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 14} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 380} \right\rbrack & \; \\{{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times e^{j\; 0}} & e^{j\;\pi} \\e^{j\; 0} & {\alpha \times e^{j\; 0}}\end{pmatrix}}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 15} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 381} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \alpha \times e^{j\; 0}} & {\beta \times e^{j\; 0}} \\{\beta \times e^{j\; 0}} & {\beta \times \alpha \times e^{j\;\pi}}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 16} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 382} \right\rbrack & \; \\{F = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times e^{j\; 0}} & e^{j\; 0} \\e^{j\; 0} & {\alpha \times e^{j\;\pi}}\end{pmatrix}}} & {{Formula}\mspace{14mu}\left( {H\; 17} \right)}\end{matrix}$

In equations (H10), (H11), (H12), (H13), (F14), (H15), (H16), and (H17),α may be either a real number or an imaginary number, and β may beeither a real number or an imaginary number. However, α is not 0 (zero).Also β is not 0 (zero), or

$\begin{matrix}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 383} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{14mu}\theta} & {\beta \times \sin\mspace{14mu}\theta} \\{\beta \times \sin\mspace{14mu}\theta} & {{- \beta} \times \cos\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 18} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 384} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\mspace{14mu}\theta} & {\sin\mspace{14mu}\theta} \\{\sin\mspace{14mu}\theta} & {{- \cos}\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 19} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 385} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \cos\mspace{14mu}\theta} & {{- \beta} \times \sin\mspace{14mu}\theta} \\{\beta \times \sin\mspace{14mu}\theta} & {\beta \times \cos\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 20} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 386} \right\rbrack & \; \\{{F = \begin{pmatrix}{\cos\mspace{14mu}\theta} & {{- \sin}\mspace{14mu}\theta} \\{\sin\mspace{14mu}\theta} & {\cos\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 21} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 387} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \sin\mspace{14mu}\theta} & {{- \beta} \times \cos\mspace{14mu}\theta} \\{\beta \times \cos\mspace{14mu}\theta} & {\beta \times \sin\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 22} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 388} \right\rbrack & \; \\{{F = \begin{pmatrix}{\sin\mspace{14mu}\theta} & {{- \cos}\mspace{14mu}\theta} \\{\cos\mspace{14mu}\theta} & {\sin\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 23} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 389} \right\rbrack & \; \\{{F = \begin{pmatrix}{\beta \times \sin\mspace{14mu}\theta} & {\beta \times \cos\mspace{14mu}\theta} \\{\beta \times \cos\mspace{14mu}\theta} & {{- \beta} \times \sin\mspace{14mu}\theta}\end{pmatrix}}{or}} & {{Formula}\mspace{14mu}\left( {H\; 24} \right)} \\\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 390} \right\rbrack & \; \\{F = \begin{pmatrix}{\sin\mspace{14mu}\theta} & {\cos\mspace{14mu}\theta} \\{\cos\mspace{14mu}\theta} & {{- \sin}\mspace{14mu}\theta}\end{pmatrix}} & {{Formula}\mspace{14mu}\left( {H\; 25} \right)}\end{matrix}$

In equations (H18), (H20), (H22), and (H24), β may be either a realnumber or an imaginary number. However, β is not 0 (zero).

or

$\begin{matrix}{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 391} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = \begin{pmatrix}{\beta \times e^{j\;{\theta_{11}{(i)}}}} & {\beta \times \alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\beta \times \alpha \times e^{j\;{\theta_{21}{(i)}}}} & {\beta \times e^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}}\end{pmatrix}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 26} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 392} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\;{\theta_{11}{(i)}}} & {\alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}} \\{\alpha \times e^{j\;{\theta_{21}{(i)}}}} & e^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}\end{pmatrix}}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 27} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 393} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = \begin{pmatrix}{\beta \times \alpha \times e^{j\;{\theta_{21}{(i)}}}} & {\beta \times e^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}}} \\{\beta \times e^{j\;{\theta_{11}{(i)}}}} & {\beta \times \alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}}\end{pmatrix}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 28} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 394} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times e^{j\;{\theta_{21}{(i)}}}} & e^{j{({{\theta_{21}{(i)}} + \lambda + \pi})}} \\e^{j\;{\theta_{11}{(i)}}} & {\alpha \times e^{j{({{\theta_{11}{(i)}} + \lambda})}}}\end{pmatrix}}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 29} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 395} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = \begin{pmatrix}{\beta \times e^{j\;\theta_{11}}} & {\alpha \times \alpha \times e^{j{({{\theta_{11}{(i)}} + {\lambda{(i)}}})}}} \\{\beta \times \alpha \times e^{j\;\theta_{21}}} & {\beta \times e^{j{({\theta_{21} + {\lambda{(i)}} + \pi})}}}\end{pmatrix}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 30} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 396} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\;\theta_{11}} & {\alpha \times e^{j{({\theta_{11} + {\lambda{(i)}}})}}} \\{\alpha \times e^{j\;\theta_{21}}} & e^{j{({\theta_{21} + {\lambda{(i)}} + \pi})}}\end{pmatrix}}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 31} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 397} \right\rbrack} & \; \\{{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\beta \times \alpha \times e^{j\;\theta_{21}}} & {\beta \times e^{j{({{\theta_{21}{(i)}} + \pi})}}} \\{\beta \times e^{j\;\theta_{11}}} & {\beta \times \alpha \times e^{j{({\theta_{11} + {\lambda{(i)}}})}}}\end{pmatrix}}}\mspace{76mu}{or}} & {{Formula}\mspace{14mu}\left( {H\; 32} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 398} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times e^{j\;\theta_{21}}} & e^{j{({{\theta_{21}{(i)}} + \pi})}} \\e^{j\;\theta_{11}} & {\alpha \times e^{j{({\theta_{11} + {\lambda{(i)}}})}}}\end{pmatrix}}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 33} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 399} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = \begin{pmatrix}{\beta \times e^{j\;\theta_{11}}} & {\alpha \times \alpha \times e^{j{({\theta_{11} + \lambda})}}} \\{\beta \times \alpha \times e^{j\;\theta_{21}}} & {\beta \times e^{j{({\theta_{21} + \lambda + \pi})}}}\end{pmatrix}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 34} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 400} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}e^{j\;\theta_{11}} & {\alpha \times e^{j{({\theta_{21} + \lambda})}}} \\{\alpha \times e^{j\;\theta_{21}}} & e^{j{({\theta_{21} + \lambda + \pi})}}\end{pmatrix}}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 35} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 401} \right\rbrack} & \; \\{\mspace{76mu}{{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\beta \times \alpha \times e^{j\;\theta_{21}}} & {\beta \times e^{j{({\theta_{21} + \lambda + \pi})}}} \\{\beta \times e^{j\;\theta_{11}}} & {\beta \times \alpha \times e^{j{({\theta_{11} + \lambda})}}}\end{pmatrix}}}\mspace{76mu}{or}}} & {{Formula}\mspace{14mu}\left( {H\; 36} \right)} \\{\mspace{76mu}\left\lbrack {{Mathematical}\mspace{14mu}{formula}\mspace{14mu} 402} \right\rbrack} & \; \\{\mspace{76mu}{{F(i)} = {\frac{1}{\sqrt{\alpha^{2} + 1}}\begin{pmatrix}{\alpha \times e^{j\;\theta_{21}}} & e^{j{({\theta_{21} + \lambda + \pi})}} \\e^{j\;\theta_{11}} & {\alpha \times e^{j{({\theta_{11} + \lambda})}}}\end{pmatrix}}}} & {{Formula}\mspace{14mu}\left( {H\; 37} \right)}\end{matrix}$

In the formulas, θ₁₁ (i), θ₂₁(i), and λ(i) are a function of i (time orfrequency), λ is a fixed value, α may be either a real number or animaginary number, and β may be either a real number or an imaginarynumber. However, α is not 0 (zero). Also β is not 0 (zero).

Each exemplary embodiment of the present disclosure can be implementedeven if a precoding matrix except for the above precoding matrix isused.

The present disclosure can widely applied to a radio system thattransmits different modulated signals from the plurality of antennas.The present disclosure can also applied to the case that the MIMOtransmission is performed in wired communication system (such as a PLC(Power Line Communication) system, an optical communication system, anda DSL (Digital Subscriber Line) system) including the plurality oftransmission points.

Thirteenth Exemplary Embodiment

The bit length adjusting method for performing the mapping processing ofan example in which the mapper performs the mapping in units of codelengths on the code length (N bits) of the code word output from theencoder is described in the first to eleventh exemplary embodiments. Themethod for applying the bit length adjusting methods of the first toeleventh exemplary embodiments to the DVB standard is described in thetwelfth exemplary embodiment.

A transmission method instead of the above bit length adjusting methodwill be described in a thirteenth exemplary embodiment.

FIG. 134 illustrates configuration of a section that generates amodulated signal in a transmitter according to a thirteenth exemplaryembodiment. In FIG. 134 , the function and signal identical to those ofthe section that generates the modulated signal of the transmitter inFIG. 5 are designated by the identical reference marks, and thedescription is omitted. s1(i) and s2(i) in FIG. 134 are transmittedwhile subjected to the above pieces of processing such as the precoding(weighting synthesis), the power change, and the phase change.

According to control signal 512, mapper 13401 performs the mapping togenerate first complex signal s1(i) (13402A) and second complex signals2(i) (13402B) from input bit string 503.

It is assumed that control signal 512 assigns the N bits as the codelength of the code word of the error correction coding processing, andassigns modulation schemes α and β as the modulation schemes used togenerated first and second complex signals s1 and s2. Modulation schemeα is one that is used to map the x-bit bit string, and modulation schemeβ is one that is used to map the y-bit bit string. (For example, BPSK isthe modulation scheme used to map the 1-bit bit string, QPSK is themodulation scheme used to map the 2-bit bit string, 16QAM is themodulation scheme used to map the 4-bit bit string, 64QAM is themodulation scheme used to map the 6-bit bit string, and 256QAM is themodulation scheme used to map the 8-bit bit string. The modulationscheme is not limited to these modulation schemes, but the abovemodulation scheme may be used.)

<Case 1> the case that code length N has 64800 bits while the set ofmodulation schemes α and β is the set of 64QAM and 256QAM (the case isreferred to as (modulation scheme α, modulation schemeβ)=(64QAM,256QAM)), <Case 2> the case that code length N has 16200 bitswhile the set of modulation schemes α and β is the set of 64QAM and256QAM ((modulation scheme α, modulation scheme β)=(64QAM,256QAM)),<Case 3> the case that code length N has 16200 bits while the set ofmodulation schemes α and β is the set of 256QAM and 256QAM ((modulationscheme α, modulation scheme β)=(256QAM,256QAM)) will be described belowwith respect to code length N (bits) assigned by control signal 512 andmodulation schemes α and β.

<Case 1>

FIG. 135 is a view illustrating an example of the mapping performed withmapper 13401 in Case 1. In FIG. 135 , a square surrounding “X” indicateseach bit of bit string 503 input to mapper 13401 (accordingly, 64800pieces of “X” exists).

Mapper 13401 maps the (x=6)-bit bit string using 64QAM to generate firstcomplex signal s1, and maps the (y=8)-bit bit string using 256QAM togenerate second complex signal s2. Mapper 13401 performs the mapping onthe total of 4626 sets from set #1 to set #4626, and one set of themapping includes the mapping of the (x=6)-bit bit string using 64QAM andthe mapping of the (y=8)-bit bit string using 256QAM.

As illustrated in FIG. 135 , because the modulation scheme for s1 of“set #1” is 64QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(64QAM,256QAM).

Similarly, “set #2” to “set #4626” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 135 ).

Therefore, in bit string 503 input to mapper 13401, 4626 sets (“set #1”to “set #4626”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×4626=64764)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #4626” are similarly expressed as (s1,s2)=(256QAM,64QAM)(see FIG. 135 ).

In “set #1” to “set #4626”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s₁ and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #4626”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

Mapper 13401 maps the remaining 36 (=64800-64764) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 64QAM and 64QAM. That is, mapper 13401 maps the (x=6)-bit bitstring using 64QAM to generate first complex signal s₁, and maps the(y=6)-bit bit string using 64QAM to generate second complex signal s2.Mapper 13401 performs the mapping on the total of 3 sets from set $1 toset $3, and 1 set of the mapping includes the mapping of the (x=6)-bitbit string using 64QAM and the mapping of the (y=6)-bit bit string using64QAM. Therefore, 3 sets (“set $1” to “set $3”) of (s₁,s2)=(64QAM,64QAM)are generated from ((6+6)×3=36)-bit bit string.

The mapping is performed using 64QAM. Alternatively, the modulationscheme (such as 64APSK) having 64 signal points may be used instead of64QAM in the I-Q plane.

Accordingly, in “set $1” to “set $3”, s₁ is one of the 64 signal pointsof the modulation scheme in the I-Q plane, and s2 is one of the 64signal points of the modulation scheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 64800 bits.

FIG. 136 is a view illustrating an example different from the mappingperformed with mapper 13401 in FIG. 135 in Case 1. The processing inFIG. 136 differs from the processing in FIG. 135 in two points. The twopoints will be described below.

The first point will be described below.

The set of modulation schemes α and β is the set of 64QAM and 256QAM,and the total of 4625 sets from set #1 to set #4625 is mapped.

As illustrated in FIG. 136 , because the modulation scheme for s1 of“set #1” is 64QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(64QAM,256QAM).

Similarly, “set #2” to “set #4625” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 136 ).

Therefore, in bit string 503 input to mapper 13401, 4625 sets (“set #1”to “set #4625”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×4625=64750)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #4625” are similarly expressed as (s₁,s2)=(256QAM,64QAM)(see FIG. 136 ).

In “set #1” to “set #4625”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #4625”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

The second point will be described below.

Mapper 13401 maps the remaining 50 (=64800−64750) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 16QAM and 64QAM. That is, mapper 13401 maps the (x=4)-bit bitstring using 16QAM to generate first complex signal s1, and maps the(y=6)-bit bit string using 64QAM to generate second complex signal s2.Mapper 13401 performs the mapping on the total of 5 sets from set $1 toset $5, and 1 set of the mapping includes the mapping of the (x=4)-bitbit string using 16QAM and the mapping of the (y=6)-bit bit string using64QAM. Therefore, 5 sets (“set $1” to “set $5”) of (s1,s2)=(16QAM,64QAM)are generated from ((4+6)×5=50)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 16QAM while the modulation scheme used to generate secondcomplex signal s2 is 64QAM. Alternatively, the modulation scheme used togenerate first complex signal s1 may be 64QAM while the modulationscheme used to generate second complex signal s2 is 16QAM. That is, “set$1” to “set $5” may be expressed as (s1,s2)=(64QAM,16QAM) (see FIG. 136).

In “set $1” to “set $5”, (s1,s2) may be either (16QAM,64QAM) or(64QAM,16QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 16QAM and 64QAM. Alternatively, themodulation scheme (such as 16APSK) having 16 signal points may be usedinstead of 16QAM in the I-Q plane, and the modulation scheme (such as64APSK) having 64 signal points may be used instead of 64QAM in the I-Qplane.

Accordingly, in “set $1” to “set $5”, s2 is one of the 64 signal pointsof the modulation scheme in the I-Q plane in the case that s1 is one ofthe 16 signal points of the modulation scheme in the I-Q plane, and s1is one of the 64 signal points of the modulation scheme in the I-Q planein the case that s2 is one of the 16 signal points of the modulationscheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 64800 bits.

FIG. 137 is a view illustrating an example different from the mappingperformed with mapper 13401 in FIGS. 135 and 136 in Case 1. Theprocessing in FIG. 137 differs from the processing in FIGS. 135 and 136in two points. The two points will be described below.

The first point will be described below.

The set of modulation schemes α and β is the set of 64QAM and 256QAM,and the total of 4628 sets from set #1 to set #4628 is mapped.

As illustrated in FIG. 137 , because the modulation scheme for s1 of“set #1” is 64QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(64QAM,256QAM).

Similarly, “set #2” to “set #4628” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 137 ).

Therefore, in bit string 503 input to mapper 13401, 4628 sets (“set #1”to “set #4628”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×4628=64792)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #4628” are similarly expressed as (s1,s2)=(256QAM,64QAM)(see FIG. 137 ).

In “set #1” to “set #4628”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #4628”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

The second point will be described below.

Mapper 13401 maps the remaining 8 (=64800-64792) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 16QAM and 16QAM. That is, mapper 13401 maps the (x=4)-bit bitstring using 16QAM to generate first complex signal s1, and maps the(y=4)-bit bit string using 16QAM to generate second complex signal s2.Mapper 13401 performs the mapping on 1 set of set $1, and 1 set of themapping includes the mapping of the (x=4)-bit bit string using 16QAM andthe mapping of the (y=4)-bit bit string using 16QAM. Therefore, 1 set(“set $1” to “set $5”) of (s₁,s2)=(16QAM,16QAM) is generated from((4+4)*1=8)-bit bit string.

The mapping is performed using 16QAM. Alternatively, the modulationscheme (such as 16APSK) having 16 signal points may be used instead of16QAM in the I-Q plane.

Accordingly, in “set $1”, s1 is one of the 16 signal points of themodulation scheme in the I-Q plane, and s2 is one of the 16 signalpoints of the modulation scheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 64800 bits.

As illustrated in FIG. 138 , mapper 13401 performs the mapping on the4628 sets in each of which the set of modulation schemes α and β is theset of 64QAM and 256QAM, and does not need to map the remaining 8 bits.

Because the modulation scheme for s1 of “set #1” is 64QAM while themodulation scheme of s2 of “set #1” is 256QAM in FIG. 138 , “set #1” isexpressed as (s1,s2)=(64QAM,256QAM) as illustrated in FIG. 137 .

Similarly, “set #2” to “set #4628” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 138 ).

Therefore, in bit string 503 input to mapper 13401, 4628 sets (“set #1”to “set #4628”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×4628=64792)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s₁ may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #4628” are similarly expressed as (s1,s2)=(256QAM,64QAM)(see FIG. 138 ).

In “set #1” to “set #4628”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #4628”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

Each of the transmission methods in FIGS. 135, 136, 137, and 138 mayindependently be performed. When code length N (bits) assigned bycontrol signal 512 and modulation schemes α and β are Case 1, mapper13401 may use the transmission method in FIG. 135 or the transmissionmethods in FIGS. 136, 137, and 138 irrespective of the coding rate ofthe error correction coding processing assigned by control signal 512.

Mapper 13401 may switch the transmission methods in FIGS. 135, 136, 137,and 138 according to the coding rate of the error correction codingprocessing assigned by control signal 512. Depending on the coding rate,mapper 13401 may use the bit string adjusting methods of the first toeleventh exemplary embodiments.

That is, one of the transmission methods is properly selected to performthe processing by the set of the error correction coding scheme, thecode length, the coding rate, and the modulation scheme.

The above description is made for the code length of 64800 bits. Forother code lengths, sometimes another piece of processing is performedsuch that a special set of the modulation schemed is inserted. In thiscase, the transmission method is similarly performed.

<Case 2>

FIG. 139 is a view illustrating an example of the mapping performed withmapper 13401 in Case 2. The processing in FIG. 139 differs from theprocessing in FIG. 135 in three points. The three points will bedescribed below.

The first point will be described below.

Bit string 503 input to mapper 13401 has bit length N of 16200 bits.

The second point will be described below.

As illustrated in FIG. 139 , because the modulation scheme for s1 of“set #1” is 64QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(64QAM,256QAM).

Similarly, “set #2” to “set #1152” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 139 ).

Therefore, in bit string 503 input to mapper 13401, 1152 sets (“set #1”to “set #1152”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×1152=16128)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #1152” are similarly expressed as (s1,s2)=(256QAM,64QAM)(see FIG. 139 ).

In “set #1” to “set #1152”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #1152”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

The third point will be described below.

Mapper 13401 maps the remaining 72 (=16200-16128) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 64QAM and 64QAM. That is, mapper 13401 maps the (x=6)-bit bitstring using 64QAM to generate first complex signal s1, and maps the(y=6)-bit bit string using 64QAM to generate second complex signal s2.Mapper 13401 performs the mapping on the total of 6 sets from set $1 toset $6, and 1 set of the mapping includes the mapping of the (x=6)-bitbit string using 64QAM and the mapping of the (y=6)-bit bit string using64QAM. Therefore, 6 sets (“set $1” to “set $6”) of (s₁,s2)=(64QAM,64QAM)are generated from ((6+6)×6=72)-bit bit string.

The mapping is performed using 64QAM. Alternatively, the modulationscheme (such as 64APSK) having 64 signal points may be used instead of64QAM in the I-Q plane.

Accordingly, in “set $1” to “set $6”, s1 is one of the 64 signal pointsof the modulation scheme in the I-Q plane, and s2 is one of the 64signal points of the modulation scheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 16200 bits.

FIG. 140 is a view illustrating an example different from the mappingperformed with mapper 13401 in FIG. 139 in Case 2. The processing inFIG. 140 differs from the processing in FIG. 139 in two points. The twopoints will be described below.

The first point will be described below.

As illustrated in FIG. 140 , because the modulation scheme for s1 of“set #1” is 64QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(64QAM,256QAM).

Similarly, “set #2” to “set #1155” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 140 ).

Therefore, in bit string 503 input to mapper 13401, 1155 sets (“set #1”to “set #1155”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×1155=16170)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #1155” are similarly expressed as (s1,s2)=(256QAM,64QAM)(see FIG. 140 ).

In “set #1” to “set #1155”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #1155”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

The second point will be described below.

Mapper 13401 maps the remaining 30 (=16200-16170) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 16QAM and 64QAM. That is, mapper 13401 maps the (x=4)-bit bitstring using 16QAM to generate first complex signal s1, and maps the(y=6)-bit bit string using 64QAM to generate second complex signal s2.Mapper 13401 performs the mapping on the total of 3 sets from set $1 toset $3, and 1 set of the mapping includes the mapping of the (x=6)-bitbit string using 64QAM and the mapping of the (y=6)-bit bit string using64QAM. Therefore, 3 sets (“set $1” to “set $3”) of (s1,s2)=(16QAM,64QAM)are generated from ((4+6)×3=30)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 16QAM while the modulation scheme used to generate secondcomplex signal s2 is 64QAM. Alternatively, the modulation scheme used togenerate first complex signal s1 may be 64QAM while the modulationscheme used to generate second complex signal s2 is 16QAM. That is, “set$1” to “set $3” may be expressed as (s1,s2)=(64QAM,16QAM) (see FIG. 140).

In “set $1” to “set $3”, (s1,s2) may be either (16QAM,64QAM) or(64QAM,16QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 16QAM and 64QAM. Alternatively, themodulation scheme (such as 16APSK) having 16 signal points may be usedinstead of 16QAM in the I-Q plane, and the modulation scheme (such as64APSK) having 64 signal points may be used instead of 64QAM in the I-Qplane.

Accordingly, in “set $1” to “set $3”, s2 is one of the 64 signal pointsof the modulation scheme in the I-Q plane in the case that s₁ is one ofthe 16 signal points of the modulation scheme in the I-Q plane, and s1is one of the 64 signal points of the modulation scheme in the I-Q planein the case that s2 is one of the 16 signal points of the modulationscheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 16200 bits.

FIG. 141 is a view illustrating an example different from the mappingperformed with mapper 13401 in FIGS. 139 and 140 in Case 2. Theprocessing in FIG. 142 differs from the processing in FIGS. 139 and 140in two points. The two points will be described below.

The first point will be described below.

As illustrated in FIG. 141 , because the modulation scheme for s1 of“set #1” is 64QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(64QAM,256QAM).

Similarly, “set #2” to “set #1156” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 141 ).

Therefore, in bit string 503 input to mapper 13401, 1156 sets (“set #1”to “set #1156”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×1156=16184)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #1156” are similarly expressed as (s1,s2)=(256QAM,64QAM)(see FIG. 141 ).

In “set $1” to “set $1156”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #1156”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

The second point will be described below.

Mapper 13401 maps the remaining 16 (=16200-16184) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 16QAM and 16QAM. That is, mapper 13401 maps the (x=4)-bit bitstring using 16QAM to generate first complex signal s1, and maps the(y=4)-bit bit string using 16QAM to generate second complex signal s2.Mapper 13401 performs the mapping on the total of 2 sets of “set $1” and“set $2”, and 1 set of the mapping includes the mapping of the (x=4)-bitbit string using 16QAM and the mapping of the (y=4)-bit bit string using16QAM. Therefore, 2 sets (“set $1” and “set $2”) of(s1,s2)=(16QAM,16QAM) are generated from ((4+4)×2=16)-bit bit string.

The mapping is performed using 16QAM. Alternatively, the modulationscheme (such as 16APSK) having 16 signal points may be used instead of16QAM in the I-Q plane.

Accordingly, in “set $1” and “set $2”, s1 is one of the 16 signal pointsof the modulation scheme in the I-Q plane, and s2 is one of the 16signal points of the modulation scheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 16200 bits.

FIG. 142 is a view illustrating an example different from the mappingperformed with mapper 13401 in FIGS. 139, 140, and 141 in Case 2. Theprocessing in FIG. 142 differs from the processing in FIGS. 139, 140,and 141 in two points. The two points will be described below.

The first point will be described below.

As illustrated in FIG. 142 , because the modulation scheme for s1 of“set #1” is 64QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(64QAM,256QAM).

Similarly, “set #2” to “set #1157” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 142 ).

Therefore, in bit string 503 input to mapper 13401, 1157 sets (“set #1”to “set #1157”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×1157=16198)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #1157” are similarly expressed as (s₁,s2)=(256QAM,64QAM)(see FIG. 142 ).

In “set #1” to “set $#1157”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #1157”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

The second point will be described below.

Mapper 13401 maps the remaining 2 (=16200-16198) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of BPSK and BPSK. That is, mapper 13401 maps the (x=1)-bit bitstring using BPSK to generate first complex signal s1, and maps the(y=1)-bit bit string using BPSK to generate second complex signal s2.Mapper 13401 performs the mapping on 1 set of set $1, and 1 set of themapping includes the mapping of the (x=4)-bit bit string using 16QAM andthe mapping of the (y=4)-bit bit string using 16QAM. Therefore, 1 set(“set $1” to “set $5”) of (s1,s2)=(BPSK, bPSK) is generated from((1+1)×1=2)-bit bit string.

The mapping is performed using BPSK. Alternatively, the modulationscheme having 2 signal points may be used instead of BPSK in the I-Qplane.

Accordingly, in “set $1”, s₁ is one of the 2 signal points of themodulation scheme in the I-Q plane, and s2 is one of the 2 signal pointsof the modulation scheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 16200 bits.

FIG. 143 is a view illustrating an example different from the mappingperformed with mapper 13401 in FIGS. 139, 140, 141, and 142 in Case 2.

As illustrated in FIG. 143 , because the modulation scheme for s1 of“set #1” is 64QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(64QAM,256QAM).

Similarly, “set #2” to “set #1157” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 142 ).

Therefore, in bit string 503 input to mapper 13401, 1157 sets (“set #1”to “set #1157”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×1157=16198)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #1157” are similarly expressed as (s1,s2)=(256QAM,64QAM)(see FIG. 143 ).

In “set #1” to “set #1157”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #1157”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

Mapper 13401 maps the remaining 2 (=16200-16198) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of QPSK and “non-mapping”. That is, mapper 13401 maps the (x=2)-bitbit string using QPSK to generate first complex signal s₁, but does notperform the mapping on second complex signal s2. Mapper 13401 performsthe mapping on 1 set of set $1, and 1 set of the mapping includes themapping of the (x=4)-bit bit string using 16QAM and the mapping of the(y=4)-bit bit string using 16QAM. Therefore, 1 set (“set $1”) of(s1,s2)=(QPSK,−) is generated from (x+y=2+0=2)-bit bit string (“−” meansthat the mapping is not performed).

In this case, the modulation scheme used to generate first complexsignal s1 is QPSK while the modulation scheme used to generate secondcomplex signal s2 is “non-mapping”. Alternatively, the modulation schemeused to generate first complex signal s1 may be “non-mapping” while themodulation scheme used to generate second complex signal s2 is QPSK.That is, “set $1” may be expressed as (s1,s2)=(−,QPSK) (see FIG. 143 ).

In “set $1”, (s1,s2) may be either (QPSK,−) or (−,QPSK) (the modulationschemes of s1 and s2 are not necessarily fixed).

The mapping is performed using QPSK. Alternatively, the modulationscheme having 4 signal points may be used instead of QPSK in the I-Qplane.

Accordingly, in “set $1”, s2 is “non-mapping” in the case that s1 is oneof the 4 signal points of the modulation scheme in the I-Q plane, and s1is “non-mapping” in the case that s2 is one of the 4 signal points ofthe modulation scheme in the I-Q plane.

Alternatively, s1 and s2 may be set to the identical signal. Therefore,in “set $1”, s2 is equal to S2 in the case that s1 is one of the 4signal points of the modulation scheme in the I-Q plane (however, thephase of s2 may be changed through the subsequent processing), and s1 isequal to s2 in the case that s2 is one of the 4 signal points of themodulation scheme in the I-Q plane (however, the phase of s1 may bechanged through the subsequent processing).

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 16200 bits.

As illustrated in FIG. 144 , mapper 13401 performs the mapping on the1157 sets from set #1 to set #1157 in each of which the set ofmodulation schemes α and β is the set of 64QAM and 256QAM, and does notneed to map the remaining 2 bits.

Because the modulation scheme for s1 of “set #1” is 64QAM while themodulation scheme of s2 of “set #1” is 256QAM in FIG. 144 , “set #1” isexpressed as (s1,s2)=(64QAM,256QAM) as illustrated in FIG. 143 .

Similarly, “set #2” to “set #1157” are expressed as(s1,s2)=(64QAM,256QAM) (see FIG. 144 ).

Therefore, in bit string 503 input to mapper 13401, 1157 sets (“set #1”to “set #1157”) of (s1,s2)=(64QAM,256QAM) are generated from((6+8)×1157=16198)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set#1” to “set #1157” are similarly expressed as (s1,s2)=(256QAM,64QAM)(see FIG. 144 ).

In “set #1” to “set #1157”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #1157”, s2 is one of the 256 signalpoints of the modulation scheme in the I-Q plane in the case that s1 isone of the 64 signal points of the modulation scheme in the I-Q plane,and s1 is one of the 256 signal points of the modulation scheme in theI-Q plane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

Each of the transmission methods in FIGS. 139, 140, 141, 142, 143, and144 may independently be performed. When code length N (bits) assignedby control signal 512 and modulation schemes α and β are Case 1, mapper13401 may use the transmission method in FIG. 139 or the transmissionmethods in FIGS. 140, 141, 142, 143, and 144 irrespective of the codingrate of the error correction coding processing assigned by controlsignal 512.

Mapper 13401 may switch the transmission methods in FIGS. 139, 140, 141,142, 143, and 144 according to the coding rate of the error correctioncoding processing assigned by control signal 512. Depending on thecoding rate, mapper 13401 may use the bit string adjusting methods ofthe first to eleventh exemplary embodiments.

That is, one of the transmission methods is properly selected to performthe processing by the set of the error correction coding scheme, thecode length, the coding rate, and the modulation scheme.

The above description is made for the code length of 16200 bits. Forother code lengths, sometimes another piece of processing is performedsuch that a special set of the modulation schemed is inserted. In thiscase, the transmission method is similarly performed.

<Case 3>

FIG. 145 is a view illustrating an example of the mapping performed withmapper 13401 in Case 3. The processing in FIG. 145 differs from theprocessing in FIG. 139 in two points. The two points will be describedbelow.

The first point will be described below.

As illustrated in FIG. 145 , because the modulation scheme for s1 of“set #1” is 256QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(256QAM,256QAM).

Similarly, “set #2” to “set #1009” are expressed as(s1,s2)=(256QAM,256QAM) (see FIG. 145 ).

Therefore, in bit string 503 input to mapper 13401, 1009 sets (“set #1”to “set #1009”) of (s1,s2)=(256QAM,256QAM) are generated from((8+8)×1009=16144)-bit bit string.

The mapping is performed using 256QAM. Alternatively, the modulationscheme (such as 256APSK) having 256 signal points may be used instead of256QAM in the I-Q plane.

Accordingly, in “set #1” to “set #1009”, s1 is one of the 256 signalpoints of the modulation scheme in the I-Q plane, and s2 is one of the256 signal points of the modulation scheme in the I-Q plane.

The second point will be described below.

Mapper 13401 maps the remaining 56 (=16200-16144) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 64QAM and 256QAM. That is, mapper 13401 maps the (x=6)-bit bitstring using 64QAM to generate first complex signal s₁, and maps the(y=8)-bit bit string using 256QAM to generate second complex signal s2.Mapper 13401 performs the mapping on the total of 4 sets from set $1 toset $4, and 1 set of the mapping includes the mapping of the (x=6)-bitbit string using 64QAM and the mapping of the (y=8)-bit bit string using256QAM. Therefore, 4 sets (“set $1” to “set $4”) of(s₁,s2)=(64QAM,256QAM) are generated from ((6+8)*4=56)-bit bit string.

In this case, the modulation scheme used to generate first complexsignal s1 is 64QAM while the modulation scheme used to generate secondcomplex signal s2 is 256QAM. Alternatively, the modulation scheme usedto generate first complex signal s1 may be 256QAM while the modulationscheme used to generate second complex signal s2 is 64QAM. That is, “set$1” to “set $4” may be expressed as (s1,s2)=(256QAM,64QAM) (see FIG. 145).

In “set $1” to “set $4”, (s1,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set $1” to “set $4”, s2 is one of the 256 signal pointsof the modulation scheme in the I-Q plane in the case that s1 is one ofthe 64 signal points of the modulation scheme in the I-Q plane, and s1is one of the 256 signal points of the modulation scheme in the I-Qplane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 16200 bits.

FIG. 146 is a view illustrating an example different from the mappingperformed with mapper 13401 in FIG. 145 in Case 3. The processing inFIG. 146 differs from the processing in FIG. 145 in two points. The twopoints will be described below.

The first point will be described below.

As illustrated in FIG. 146 , because the modulation scheme for s1 of“set #1” is 256QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(256QAM,256QAM).

Similarly, “set #2” to “set #1011” are expressed as(s1,s2)=(256QAM,256QAM) (see FIG. 146 ).

Therefore, in bit string 503 input to mapper 13401, 1011 sets (“set #1”to “set #1011”) of (s1,s2)=(256QAM,256QAM) are generated from((8+8)×1011=16176)-bit bit string.

The mapping is performed using 256QAM. Alternatively, the modulationscheme (such as 256APSK) having 256 signal points may be used instead of256QAM in the I-Q plane.

Accordingly, in “set #1” to “set #1011”, s1 is one of the 256 signalpoints of the modulation scheme in the I-Q plane, and s2 is one of the256 signal points of the modulation scheme in the I-Q plane.

The second point will be described below.

Mapper 13401 maps the remaining 24 (=16200−16176) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 64QAM and 64QAM. That is, mapper 13401 maps the (x=6)-bit bitstring using 64QAM to generate first complex signal s1, and maps the(y=6)-bit bit string using 64QAM to generate second complex signal s2.Mapper 13401 performs the mapping on the total of 2 sets of set $1 andset $2, and 1 set of the mapping includes the mapping of the (x=4)-bitbit string using 16QAM and the mapping of the (y=4)-bit bit string using16QAM. Therefore, 2 sets (“set $1” and “set $2”) of(s1,s2)=(64QAM,64QAM) are generated from ((6+6)×2=24)-bit bit string.

The mapping is performed using 64QAM. Alternatively, the modulationscheme having 64 signal points may be used instead of 64QAM in the I-Qplane.

Accordingly, in “set $1” and “set $2”, s1 is one of the 64 signal pointsof the modulation scheme in the I-Q plane, and s2 is one of the 64signal points of the modulation scheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 16200 bits.

FIG. 147 is a view illustrating an example different from the mappingperformed with mapper 13401 in FIGS. 145 and 146 in Case 3. Theprocessing in FIG. 147 differs from the processing in FIGS. 145 and 146in two points. The two points will be described below.

The first point will be described below.

As illustrated in FIG. 147 , because the modulation scheme for s1 of“set #1” is 256QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(256QAM,256QAM).

Similarly, “set #2” to “set #1012” are expressed as(s1,s2)=(256QAM,256QAM) (see FIG. 147 ).

Therefore, in bit string 503 input to mapper 13401, 1012 sets (“set #1”to “set #1012”) of (s1,s2)=(256QAM,256QAM) are generated from((8+8)×1012=16192)-bit bit string.

The mapping is performed using 256QAM. Alternatively, the modulationscheme (such as 256APSK) having 256 signal points may be used instead of256QAM in the I-Q plane.

Accordingly, in “set #1” to “set #1012”, s1 is one of the 256 signalpoints of the modulation scheme in the I-Q plane, and s2 is one of the256 signal points of the modulation scheme in the I-Q plane.

The second point will be described below.

Mapper 13401 maps the remaining 8 (=16200-16192) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 16QAM and 16QAM. That is, mapper 13401 maps the (x=4)-bit bitstring using 16QAM to generate first complex signal s₁, and maps the(y=4)-bit bit string using 16QAM to generate second complex signal s2.Mapper 13401 performs the mapping on 1 set of set $1, and 1 set of themapping includes the mapping of the (x=4)-bit bit string using 16QAM andthe mapping of the (y=4)-bit bit string using 16QAM. Therefore, 1 set(“set $1” to “set $5”) of (s₁,s2)=(16QAM,16QAM) is generated from((4+4)*1=8)-bit bit string.

The mapping is performed using 16QAM. Alternatively, the modulationscheme having 16 signal points may be used instead of 16QAM in the I-Qplane.

Accordingly, in “set $1”, s1 is one of the 16 signal points of themodulation scheme in the I-Q plane, and s2 is one of the 16 signalpoints of the modulation scheme in the I-Q plane.

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 16200 bits.

FIG. 148 is a view illustrating an example different from the mappingperformed with mapper 13401 in FIGS. 145, 146, and 147 in Case 3.

As illustrated in FIG. 148 , because the modulation scheme for s1 of“set #1” is 256QAM while the modulation scheme of s2 of “set #1” is256QAM, “set #1” is expressed as (s1,s2)=(256QAM,256QAM).

Similarly, “set #2” to “set #1012” are expressed as(s1,s2)=(256QAM,256QAM) (see FIG. 148 ).

Therefore, in bit string 503 input to mapper 13401, 1012 sets (“set #1”to “set #1012”) of (s1,s2)=(256QAM,256QAM) are generated from((8+8)×1012=16192)-bit bit string.

The mapping is performed using 256QAM. Alternatively, the modulationscheme (such as 256APSK) having 256 signal points may be used instead of256QAM in the I-Q plane.

Accordingly, in “set #1” to “set #1012”, s1 is one of the 256 signalpoints of the modulation scheme in the I-Q plane, and s2 is one of the256 signal points of the modulation scheme in the I-Q plane.

Mapper 13401 maps the remaining 8 (=16200-16192) bits of input bitstring 503 while switching the set of modulation schemes α and β to theset of 256QAM and “non-mapping”. That is, mapper 13401 maps the(x=8)-bit bit string using 256QAM to generate first complex signal s1,but does not perform the mapping on second complex signal s2. Mapper13401 performs the mapping on 1 set of set $1, and 1 set of the mappingincludes the mapping of the (x=4)-bit bit string using 16QAM and themapping of the (y=4)-bit bit string using 16QAM. Therefore, 1 set (“set$1”) of (s1,s2)=(256QAM,−) is generated from (x+y=8+0=8)-bit bit stringmeans that the mapping is not performed).

In this case, the modulation scheme used to generate first complexsignal s1 is 256QAM while the modulation scheme used to generate secondcomplex signal s2 is “non-mapping”. Alternatively, the modulation schemeused to generate first complex signal s1 may be “non-mapping” while themodulation scheme used to generate second complex signal s2 is 256QAM.That is, “set $1” may be expressed as (s1,s2)=(−,256QAM) (see FIG. 148).

In “set $1”, (s1,s2) may be either (256QAM,−) or (−,256QAM) (themodulation schemes of s₁ and s2 are not necessarily fixed).

The mapping is performed using 256QAM. Alternatively, the modulationscheme having 256 signal points may be used instead of 256QAM in the I-Qplane.

Accordingly, in “set $1”, s2 is “non-mapping” in the case that s₁ is oneof the 256 signal points of the modulation scheme in the I-Q plane, ands1 is “non-mapping” in the case that s2 is one of the 256 signal pointsof the modulation scheme in the I-Q plane.

Alternatively, s1 and s2 may be set to the identical signal. Therefore,in “set $1”, s2 is equal to s2 in the case that s1 is one of the 256signal points of the modulation scheme in the I-Q plane (however, thephase of s2 may be changed through the subsequent processing), and s1 isequal to s2 in the case that s2 is one of the 256 signal points of themodulation scheme in the I-Q plane (however, the phase of s1 may bechanged through the subsequent processing).

Accordingly, mapper 13401 can generate the symbol set in units of codelengths each of which has the input 16200 bits.

As illustrated in FIG. 149 , mapper 13401 performs the mapping on the1012 sets from set #1 to set #1012 in each of which the set ofmodulation schemes α and β is the set of 256QAM and 256QAM, and does notneed to map the remaining 8 bits.

Because the modulation scheme for s1 of “set #1” is 256QAM while themodulation scheme of s2 of “set #1” is 256QAM in FIG. 149 , “set #1” isexpressed as (s1,s2)=(256QAM,256QAM) as illustrated in FIG. 148 .

Similarly, “set #2” to “set #1012” are expressed as(s1,s2)=(256QAM,256QAM) (see FIG. 149 ).

Therefore, in bit string 503 input to mapper 13401, 1012 sets (“set #1”to “set #1012”) of (s1,s2)=(256QAM,256QAM) are generated from((8+8)×1012=16192)-bit bit string.

The mapping is performed using 256QAM. Alternatively, the modulationscheme (such as 256APSK) having 256 signal points may be used instead of256QAM in the I-Q plane.

Accordingly, in “set #1” to “set #1012”, s1 is one of the 256 signalpoints of the modulation scheme in the I-Q plane, and s2 is one of the256 signal points of the modulation scheme in the I-Q plane.

Each of the transmission methods in FIGS. 145, 146, 147, 148, and 149may independently be performed. When code length N (bits) assigned bycontrol signal 512 and modulation schemes α and β are Case 1, mapper13401 may use the transmission method in FIG. 145 or the transmissionmethods in FIGS. 146, 147, 148, and 149 irrespective of the coding rateof the error correction coding processing assigned by control signal512.

Mapper 13401 may switch the transmission methods in FIGS. 145, 146, 147,148 , and 149 according to the coding rate of the error correctioncoding processing assigned by control signal 512. Depending on thecoding rate, mapper 13401 may use the bit string adjusting methods ofthe first to eleventh exemplary embodiments.

That is, one of the transmission methods is properly selected to performthe processing by the set of the error correction coding scheme, thecode length, the coding rate, and the modulation scheme.

The above description is made for the code length of 16200 bits. Forother code lengths, sometimes another piece of processing is performedsuch that a special set of the modulation schemed is inserted. In thiscase, the transmission method is similarly performed.

As described above, s1 and s2 (s1(i) and s2(i)) generated in FIGS. 135to 149 are transmitted while subjected to the above pieces of processingsuch as the precoding (weighting synthesis), the power change, and thephase change.

Alternatively, the space-time block code (sometimes referred to as MISOtransmission scheme or transmission diversity) may be performed on s1and s2 (s1(i) and s2(i)) generated in FIGS. 135 to 149 (for example, seeFIGS. 150 and 161 ).

The space-time block coding in FIG. 150 will be described below (thespace-time block coding in FIG. 161 is described later).

Mapped signal 15001 is input to MISO processor 15002, and MISO processor15002 outputs post-MISO-processing signals 15003A and 15003B.

For example, mapped signal 15001 input to MISO processor 15002 is set tofirst and second complex signal s1(i) and s2(i) obtained through themapping processing (i is an integer larger than 0). Post-MISO-processing signal 15003A is s1(i) in slot 2i, and is s2(i) in slot(2i+1). Post-MISO-processing signal 15003B is −s2*(i) in slot 2i, and iss1*(i) in slot (2i+1). The mark “·” means a complex conjugate.

This can be reworded as follows. It is assumed that mapped signal 15001is arranged in the order of (s1 (1),s2(1)), (s1(2),s2(2)),(s1(3),s2(3)), . . . , (s1(i),s2(i)), . . . (i is an integer larger than0). For example, post-MISO-processing signal 15003A is s1(1), s2(1), s1(2), s2(2), s1 (3), s2(3), . . . , s1(i), s2(i), . . . , and post-MISO-processing signal 15003B is −s2*(1), s1*(1), −s2*(2), s1*(2),−s2*(3), s1*(3), . . . , −s2*(i), s1*(i), . . . .

At this point, post-M ISO-processing signals 15003A and 15003Bcorrespond to post-processing baseband signals 12502A and 12502B in FIG.125 , respectively. The space-time block coding method is not limited tothe above method.

<Case 4> and <Case 5> will be described below as an example in which thespace-time block code is applied.

<Case 4>

In the case that code length N has the 16200 bits while the set ofmodulation schemes α and β is the set of 256QAM and 256QAM similarly to<Case 3>, the transmission method is used is performed on generatedfirst and second complex signals s1(i) and s2(i) using the space-timeblock code.

FIG. 151 is a view illustrating an example of the processing performingthe space-time block code on the processing in FIG. 145 .

In FIG. 151 , because the modulation scheme sets “set #1” to “set #1009”are similar to those in FIG. 145 , the description is omitted (althoughthe case of 256QAM is described by way of example in FIG. 151 , the setof modulation schemes is not limited to the case of 256QAM as describedin FIG. 145 ).

In “set #1” to “set #1009”, it is assumed that complex signal set “set#i” is expressed as (s1(i),s2(i)) (i is an integer from 1 to 1009). Whenthe MISO processing is performed on complex signal sets (s1(1),s2(1)),(s1(2),s2(2)), . . . , (s1(1009),s2(1009)), the set ofpost-MISO-processing signals 15003A and 15003B is

(s1 (1),−s2*(1)) in slot 2,

(s2(1),s1*(1)) in slot 3,

(s1(2),−s2*(2)) in slot 4,

(s2(2),s1*(2)) in slot 5,

. . . ,

(s1 (1009),−s2*(1009)) in slot 2018, and

(s2(1009),s1*(1009)) in slot 2019

(signals from slots 2 to 2019).

In FIG. 151 , because the modulation scheme sets “set $1” to “set $4”are similar to those in FIG. 145 , the description is omitted (althoughthe case of 64QAM and 256QAM is described by way of example in FIG. 151, the set of modulation schemes is not limited to the case of 64QAM and256QAM as described in FIG. 145 ).

It is assumed that complex signal sets “set $1”, “set $2”, “set $3”, and“set $4” are expressed as (s1 (1010),s2(1010)), (s1 (1011),s2(1011)),(s1 (1012),s2(1012)), and (s1 (1013),s2(1013)), respectively. When theMISO processing is performed on complex signal sets (s1(1010),s2(1010)), (s1 (1011),s2(1011)), (s1 (1012),s2(1012)), and (s1(1013),s2(1013)), the set of post-MISO-processing signals 15003A and15003B is (s1 (1010),−s2*(1010)) in slot 2020,

(s2(1010),s1*(1010)) in slot 2021,

(s1 (1011),−s2*(1011)) in slot 2022,

(s2(1011),s1*(1011)) in slot 2023,

(s1 (1012),−s2*(1012)) in slot 2024,

(s2(1012),s1*(1012)) in slot 2025,

(s1 (1013),−s2*(1013)) in slot 2026, and

(s2(1013),s1*(1013)) in slot 2027

(signals from slots 2020 to 2027).

FIG. 152 is a view illustrating an example of the processing performingthe space-time block code on the processing in FIG. 146 .

In FIG. 152 , because the modulation scheme sets “set #1” to “set #1011”are similar to those in FIG. 146 , the description is omitted (althoughthe case of 256QAM is described by way of example in FIG. 152 , the setof modulation schemes is not limited to the case of 256QAM as describedin FIG. 146 ).

In “set #1” to “set #1011”, it is assumed that complex signal set “set#i” is expressed as (s1 (i),s2(i)) (i is an integer from 1 to 1011).When the MISO processing is performed on complex signal sets(s1(1),s2(1)), (s1(2),s2(2)), . . . , (s1 (1011),s2(1011)), the set ofpost-MISO-processing signals 15003A and 15003B is (s1 (1),−s2*(1)) inslot 2, (s2(1),s1*(1)) in slot 3, (s1 (2),−s₂*(2)) in slot 4,(s2(2),s1*(2)) in slot 5, . . . , (s1 (1011),−s2*(1011)) in slot 2022,and (s2(1011),s1*(1011)) in slot 2023 (signals from slots 2 to 2023).

In FIG. 152 , because the modulation scheme sets “set $1” and “set $2”are similar to those in FIG. 146 , the description is omitted (althoughthe case of 64QAM is described by way of example in FIG. 152 , the setof modulation schemes is not limited to the case of 64QAM as describedin FIG. 146 ).

It is assumed that complex signal sets “set $1” and “set $2” areexpressed as (s1 (1012),s2(1012)) and (s1 (1013),s2(1013)),respectively. When the MISO processing is performed on complex signalsets (s1 (1012),s2(1012)) and (s1 (1013),s2(1013)), the set ofpost-MISO-processing signals 15003A and 15003B is

(s1 (1012),−s2*(1012)) in slot 2024,

(s2(1012),s1*(1012)) in slot 2025,

(s1 (1013),−s2*(1013)) in slot 2026, and

(s2(1013),s1*(1013)) in slot 2027

(signals from slots 2024 to 2027).

FIG. 153 is a view illustrating an example of the processing performingthe space-time block code on the processing in FIG. 147 .

In FIG. 153 , because the modulation scheme sets “set #1” to “set #1012”are similar to those in FIG. 147 , the description is omitted (althoughthe case of 256QAM is described by way of example in FIG. 153 , the setof modulation schemes is not limited to the case of 256QAM as describedin FIG. 147 ).

In “set #1” to “set #1012”, it is assumed that complex signal set “set#i” is expressed as (s1(i),s2(i)) (i is an integer from 1 to 1012). Whenthe MISO processing is performed on complex signal sets (s1(1),s2(1)),(s1(2),s2(2)), . . . , (s1 (1012),s2(1012)), the set ofpost-MISO-processing signals 15003A and 15003B is

(s1 (1),−s2*(1)) in slot 2,

(s2(1),s1*(1)) in slot 3,

(s1(2),−s2*(2)) in slot 4,

(s2(2),s1*(2)) in slot 5,

. . . ,

(s1 (1011),−s2*(1011)) in slot 2022,

(s2(1011),s1*(1011)) in slot 2023,

(s1 (1012),−s2*(1012)) in slot 2024, and

(s2(1012),s1*(1012)) in slot 2025

(signals from slots 2 to 2025).

In FIG. 153 , because the modulation scheme set “set #1” is similar tothose in FIG. 147 , the description is omitted (although the case of16QAM is described by way of example in FIG. 153 , the set of modulationschemes is not limited to the case of 16QAM as described in FIG. 147 ).

It is assumed that complex signal set “set $1” is expressed as (s1(1013),s2(1013)). When the MISO processing is performed on complexsignal set (s1 (1013),s2(1013)), the set of post-MISO-processing signals15003A and 15003B is

s1 (1013),−s2*(1013)) in slot 2026 and

(s2(1013),s1*(1013)) in slot 2027

(signals from slots 2026 and 2027).

FIG. 154 is a view illustrating an example of the processing performingthe space-time block code on the processing in FIG. 148 .

In FIG. 154 , because the modulation scheme sets “set #1” to “set #1012”are similar to those in FIG. 148 , the description is omitted (althoughthe case of 256QAM is described by way of example in FIG. 154 , the setof modulation schemes is not limited to the case of 256QAM as describedin FIG. 148 ).

In “set #1” to “set #1012”, it is assumed that complex signal set “set#i” is expressed as (s1(i),s2(i)) (i is an integer from 1 to 1012). Whenthe MISO processing is performed on complex signal sets (s1(1),s2(1)),(s1(2),s2(2)), . . . , (s1 (1012),s2(1012)), the set ofpost-MISO-processing signals 15003A and 15003B is

(s1 (1),−s2*(1)) in slot 2,

(s2(1),s1*(1)) in slot 3,

(s1(2),−s2*(2)) in slot 4,

(s2(2),s1*(2)) in slot 5,

. . . ,

(s1 (1011),−s2*(1011)) in slot 2022,

(s2(1011),s1*(1011)) in slot 2023,

(s₁ (1012),−s2*(1012)) in slot 2024, and

(s2(1012),s1*(1012)) in slot 2025

(signals from slots 2 to 2025).

In FIG. 154 , because the modulation scheme set “set #1” is similar tothose in FIG. 148 , the description is omitted (although the case of“256QAM” and “non-mapping” is described by way of example in FIG. 154 ,the set of modulation schemes is not limited to the case of 16QAM asdescribed in FIG. 148 ).

Because there are the plurality of transmission methods, thetransmission methods will be described below.

Method 154-1: It is assumed that complex signal set “set $1” isexpressed as (s1 (1013),s2(1013)). When the MISO processing is performedon complex signal set (s1 (1013),s2(1013)), the set ofpost-MISO-processing signals 15003A and 15003B is (s1 (1013),−s2*(1013))in slot 2026 and (s2(1013),s1*(1013)) in slot 2027 (signals from slots2026 and 2027).Method 154-2: It is assumed that complex signal set “set $1” isexpressed as (s₁ (1013),s2(1013)).

8 bits are transmitted using s1, but the bit is not transmitted usings2. At this point, the set of signals 15003A and 15003B is set to

(s1 (1013),0) in slot 2026

without performing the MISO processing.

Otherwise 8 bits are transmitted using s2, but the bit is nottransmitted using s1. At this point, the set of signals 15003A and15003B is set to

(0,s2(1013)) in slot 2026

without performing the MISO processing.

Method 154-3: It is assumed that complex signal set “set $1” isexpressed as (s₁ (1013),s2(1013)).

It is assumed that 8 bits are transmitted using s₁, and that similarly 8bits are transmitted using s2. At this point, the set of signals 15003Aand 15003B is set to (s₁ (1013),s2(1013)=s₁ (1013)) in slot 2026

without performing the MISO processing.

FIG. 155 is a view illustrating the processing performing the space-timeblock code on the processing in FIG. 149 .

In FIG. 155 , because the modulation scheme sets “set #1” to “set #1012”are similar to those in FIG. 149 , the description is omitted (althoughthe case of 256QAM is described by way of example in FIG. 155 , the setof modulation schemes is not limited to the case of 256QAM as describedin FIG. 149 ).

In “set #1” to “set #1012”, it is assumed that complex signal set “set#i” is expressed as (s1(i),s2(i)) (i is an integer from 1 to 1012). Whenthe MISO processing is performed on complex signal sets (s1(1),s2(1)),(s₁(2),s2(2)), . . . , (s1 (1012),s2(1012)), the set ofpost-MISO-processing signals 15003A and 15003B is

(s1 (1),−s2*(1)) in slot 2,

(s2(1),s1*(1)) in slot 3,

(s1(2),−s2*(2)) in slot 4,

(s2(2),s1*(2)) in slot 5,

. . . ,

(s1 (1011),−s2*(1011)) in slot 2022,

(s2(1011),s1*(1011)) in slot 2023,

(s1 (1012),−s2*(1012)) in slot 2024, and

(s2(1012),s1*(1012)) in slot 2025

(signals from slots 2 to 2025).

The remaining 8 bits are not transmitted.

The above description is made for the code length of 16200 bits. Forother code lengths, sometimes another piece of processing is performedsuch that a special set of the modulation schemed is inserted. In thiscase, the transmission method is similarly performed.

<Case 5>

The processing different from <Case 4>, which is performed with mapper13401, in the case that the plurality of code blocks each of which hascode length N of 16200 bits are continuously arranged while the set ofmodulation schemes α and β is the set of 256QAM and 256QAM will bedescribed below.

FIG. 156 is a view illustrating the processing performed with mapper13401 in the case that the code block having code length N of 16200 bitsis an even number (therefore, the number of code blocks is set to 2g (gis a natural number)) while the set of modulation schemes α and β (theset of (modulation scheme of s₁, modulation scheme of s2)) is the set of256QAM and 256QAM.

In FIG. 156 , although “set #1” to “set #2025g” exist, and “set” meansthe set of (s1,s2), and is expressed as (s1,s2)=(256QAM,256QAM) because(modulation scheme of s1, modulation scheme of s2) is (256QAM,256QAM).

The number of bits of all the blocks becomes (16200×2g=32400×g) becausethe number of code blocks is 2g, and ((32400×g)/16=2025×g) sets existbecause of (x+y=8+8=16) obtained from the set of 256QAM and 256QAM,which is of the set of modulation schemes α and β.

The mapping is performed using 256QAM. Alternatively, the modulationscheme (such as 256APSK) having 256 signal points may be used instead of256QAM in the I-Q plane.

Accordingly, in “set #1” to “set #2025g”, s1 is one of the 256 signalpoints of the modulation scheme in the I-Q plane, and s2 is one of the256 signal points of the modulation scheme in the I-Q plane.

As described in <Case 4>, the MISO processing is performed using the setof s1 and s2 in each of sets “set #1” to “set #2025g”, and thetransmitter transmits the set of post-MISO-processing signals 15003A and15003B.

Accordingly, mapper 13401 maps the total of 2025g sets from set #1 toset #2025g, which allows the transmission of the data. “Set #1” to “set#2025g” may be generated from (32400×g) bits by any method.

FIG. 157 is a view illustrating the processing performed with mapper13401 in the case that the code block having code length N of 16200 bitsis an odd number (therefore, the number of code blocks is set to (2g+1)(g is an integer larger than 0)) while the set of modulation schemes αand β (the set of (modulation scheme of s1, modulation scheme of s2)) isthe set of 256QAM and 256QAM or the set of 64QAM and 256QAM.

In FIG. 157 , although “set #1” to “set #(2025×g+1009)” and “set $1” to“set $4” exist, the set of (modulation scheme of s1, modulation schemeof s2) in “set #1” to “set #(2025×g+1009)” is expressed as(s1,s2)=(256QAM,256QAM), and the set of (modulation scheme of s₁,modulation scheme of s2) in “set $1” to “set $4” is expressed as(s1,s2)=(64QAM,256QAM).

In FIG. 157 , the set of (modulation scheme of s1, modulation scheme ofs2) in “set #1” to “set #(2025×g+1009)” is expressed as(s1,s2)=(256QAM,256QAM). Alternatively, the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #(2025×g+1009)”, s₁ is one of the 256signal points of the modulation scheme in the I-Q plane, and s2 is oneof the 256 signal points of the modulation scheme in the I-Q plane.

As described in <Case 4>, the MISO processing is performed using the setof s1 and s2 in each of sets “set #1” to “set #(2025×g+1009)”, and thetransmitter transmits the set of post-MISO-processing signals 15003A and15003B.

In FIG. 157 , although the set of (modulation scheme of s1, modulationscheme of s2) in “set $1” to “set $4” is expressed as(s1,s2)=(64QAM,256QAM), (s₁,s2) may be either (64QAM,256QAM) or(256QAM,64QAM) (the modulation schemes of s1 and s2 are not necessarilyfixed).

The mapping is performed using 64QAM and 256QAM. Alternatively, themodulation scheme (such as 64APSK) having 64 signal points may be usedinstead of 64QAM in the I-Q plane, and the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set $1” to “set $4”, s2 is one of the 256 signal pointsof the modulation scheme in the I-Q plane in the case that s1 is one ofthe 64 signal points of the modulation scheme in the I-Q plane, and s1is one of the 256 signal points of the modulation scheme in the I-Qplane in the case that s2 is one of the 64 signal points of themodulation scheme in the I-Q plane.

As described in <Case 4>, the MISO processing is performed using the setof s1 and s2 in each of sets “set $1” to “set $4”, and the transmittertransmits the set of post-MISO-processing signals 15003A and 15003B.

FIG. 158 is a view illustrating the processing performed with mapper13401 in the case that the code block having code length N of 16200 bitsis an odd number (therefore, the number of code blocks is set to (2g+1)(g is an integer larger than 0)) while the set of modulation schemes αand β (the set of (modulation scheme of s1, modulation scheme of s2)) isthe set of 256QAM and 256QAM or the set of 64QAM and 64QAM.

In FIG. 158 , although “set #1” to “set #(2025×g+1011)” and “set$1” and“set $2” exist, the set of (modulation scheme of s1, modulation schemeof s2) in “set #1” to “set #(2025×g+1011)” is expressed as(s1,s2)=(256QAM,256QAM), and the set of (modulation scheme of s1,modulation scheme of s2) in “set $1” and “set $2” is expressed as(s1,s2)=(64QAM,64QAM).

In FIG. 158 , the set of (modulation scheme of s1, modulation scheme ofs2) in “set #1” to “set #(2025×g+1011)” is expressed as(s1,s2)=(256QAM,256QAM). Alternatively, the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #(2025×g+1011)”, s1 is one of the 256signal points of the modulation scheme in the I-Q plane, and s2 is oneof the 256 signal points of the modulation scheme in the I-Q plane.

As described in <Case 4>, the MISO processing is performed using the setof s1 and s2 in each of sets “set #1” to “set #(2025×g+1011)”, and thetransmitter transmits the set of post-MISO-processing signals 15003A and15003B.

In FIG. 158 , the set of (modulation scheme of s1, modulation scheme ofs2) in “set $1” and “set $2” is expressed as (s1,s2)=(64QAM,64QAM).Alternatively, the modulation scheme (such as 64APSK) having 64 signalpoints may be used instead of 64QAM in the I-Q plane.

Accordingly, in “set $1” and “set $2”, s1 is one of the 64 signal pointsof the modulation scheme in the I-Q plane, and s2 is one of the 64signal points of the modulation scheme in the I-Q plane.

As described in <Case 4>, the MISO processing is performed using the setof s1 and s2 in each of sets “set $1” and “set $2”, and the transmittertransmits the set of post-MISO-processing signals 15003A and 15003B.

FIG. 159 is a view illustrating the processing performed with mapper13401 in the case that the code block having code length N of 16200 bitsis an odd number (therefore, the number of code blocks is set to (2g+1)(g is an integer larger than 0)) while the set of modulation schemes αand β (the set of (modulation scheme of s1, modulation scheme of s2)) isthe set of 256QAM and 256QAM or the set of 16QAM and 16QAM.

In FIG. 159 , although “set #1” to “set #(2025×g+1012)” and “set $1”exist, the set of (modulation scheme of s1, modulation scheme of s2) in“set #1” to “set #(2025×g+1012)” is expressed as(s1,s2)=(256QAM,256QAM), and the set of (modulation scheme of s1,modulation scheme of s2) in “set $1” is expressed as(s1,s2)=(16QAM,16QAM).

In FIG. 159 , the set of (modulation scheme of s1, modulation scheme ofs2) in “set #1” to “set #(2025×g+1012)” is expressed as(s1,s2)=(256QAM,256QAM). Alternatively, the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #(2025×g+1012)”, s1 is one of the 256signal points of the modulation scheme in the I-Q plane, and s2 is oneof the 256 signal points of the modulation scheme in the I-Q plane.

As described in <Case 4>, the MISO processing is performed using the setof s1 and s2 in each of sets “set #1” to “set #(2025×g+1012)”, and thetransmitter transmits the set of post-MISO-processing signals 15003A and15003B.

In FIG. 159 , the set of (modulation scheme of s1, modulation scheme ofs2) in “set $1” is expressed as (s1,s2)=(16QAM,16QAM). Alternatively,the modulation scheme (such as 16APSK) having 16 signal points may beused instead of 16QAM in the I-Q plane.

Accordingly, in “set $1”, s1 is one of the 16 signal points of themodulation scheme in the I-Q plane, and s2 is one of the 16 signalpoints of the modulation scheme in the I-Q plane.

As described in <Case 4>, the MISO processing is performed using the setof s1 and s2 in “set $1”, and the transmitter transmits the set ofpost-MISO-processing signals 15003A and 15003B.

FIG. 160 is a view illustrating the processing performed with mapper13401 in the case that the code block having code length N of 16200 bitsis an odd number (therefore, the number of code blocks is set to (2g+1)(g is an integer larger than 0)) while the set of modulation schemes αand β (the set of (modulation scheme of s1, modulation scheme of s2)) isthe set of 256QAM and 256QAM or the set of 256QAM and “non-mapping” (inFIG. 160 , “non-mapping” is indicated by mark

In FIG. 160 , although “set #1” to “set #(2025×g+1012)” and “set $1”exist, the set of (modulation scheme of s1, modulation scheme of s2) in“set #1” to “set #(2025×g+1012)” is expressed as(s1,s2)=(256QAM,256QAM), and the set of (modulation scheme of s1,modulation scheme of s2) in “set $1” is expressed as (s1,s2)=(256QAM,−)or (—,256QAM).

In FIG. 160 , the set of (modulation scheme of s1, modulation scheme ofs2) in “set #1” to “set #(2025×g+1012)” is expressed as(s1,s2)=(256QAM,256QAM). Alternatively, the modulation scheme (such as256APSK) having 256 signal points may be used instead of 256QAM in theI-Q plane.

Accordingly, in “set #1” to “set #(2025×g+1012)”, s1 is one of the 256signal points of the modulation scheme in the I-Q plane, and s2 is oneof the 256 signal points of the modulation scheme in the I-Q plane.

As described in <Case 4>, the MISO processing is performed using the setof s1 and s2 in each of sets “set #1” to “set #(2025×g+1012)”, and thetransmitter transmits the set of post-MISO-processing signals 15003A and15003B.

In FIG. 160 , the set of (modulation scheme of s1, modulation scheme ofs2) in “set $1” is expressed as (s1,s2)=(256QAM,−) or (—,256QAM).Alternatively, the modulation scheme (such as 256APSK) having 256 signalpoints may be used instead of 256QAM in the I-Q plane.

Accordingly, in “set $1”, s2 is “non-mapping” in the case that s1 is oneof the 256 signal points of the modulation scheme in the I-Q plane, ands1 is “non-mapping” in the case that s2 is one of the 256 signal pointsof the modulation scheme in the I-Q plane.

A plurality of transmission methods with respect to the “set $1”transmitting method in FIG. 160 will be described below.

Method 160-1:

It is assumed that complex signal set “set $1” is expressed as (s1,s2).

When the MISO processing is performed on complex signal set (s1,s2),(s1,−s2*) is transmit as the set of post-MISO-processing signals 15003Aand 15003B in the first slot. (s2,s1*) is transmitted in the second slotof “set $1”.

Method 160-2:

It is assumed that complex signal set “set $1” is expressed as (s1,s2).

At this point, “set $1” is transmitted by one slot.

8 bits are transmitted using s1, but the bit is not transmitted usings2. At this point, the set of signals 15003A and 15003B is set to

(s1,0) in the first slot of “set $1”

without performing the MISO processing.

Otherwise 8 bits are transmitted using s2, but the bit is nottransmitted using s1. At this point, the set of signals 15003A and15003B is set to

(0,s2) in the first slot of “set $1”

without performing the MISO processing.

Method 160-3:

It is assumed that complex signal set “set $1” is expressed as (s1,s2).At this point, “set $1” is transmitted by one slot.

It is assumed that 8 bits are transmitted using s1, and that similarly 8bits are transmitted using s2. At this point, the set of signals 15003Aand 15003B is set to (s1,s2=s1) in the first slot of “set $1”

without performing the MISO processing (however, the phase of s1 and/ors2 may be changed through the subsequent processing).

In Case 5, the description is made while the number of code blocks isdivided into the even number and the odd number. For example, thetransmitter counts the number of code blocks existing in the frame, andperforms one of the pieces of processing for the even and odd numbers.

The case that the code length has the 16200 bits while (256QAM,256QAM)is included in (modulation scheme of s1, modulation scheme of s2) isdescribed above. Alternatively, depending on the number of code blocks,there is a transmission method in which the slot for the space-timeblock coding and a slot for special processing are provided.

Modification of Transmission Method with Space-Time Block Code>

The method of the space-time block code (sometimes referred to as MISOtransmission scheme or transmission diversity) is not limited to theconfiguration in FIG. 150 , but the space-time block code may betransmitted as illustrated in FIG. 161 (because the operation in FIG.161 is similar to that in FIG. 150 , the component is designated by theidentical reference mark).

Mapped signal 15001 is input to MISO processor 15002, and MISO processor15002 outputs post-MISO-processing signals 15003A and 15003B.

For example, mapped signal 15001 input to MISO processor 15002 is set tofirst and second complex signal s1(i) and s2(i) obtained through themapping processing (i is an integer larger than 0). Post-MISO-processingsignal 15003A is s1(i) in slot 2i, and is −s2*(i) in slot (2i+1).Post-MISO-processing signal 15003B is s2(i) in slot 2i, and is s1*(i) inslot (2i+1). The mark “*” means a complex conjugate.

This can be reworded as follows. It is assumed that mapped signal 15001is arranged in the order of (s1 (1),s2(1)), (s1(2),s2(2)),(s1(3),s2(3)), . . . , (s1(i),s2(i)), . . . (i is an integer larger than0). For example, post-MISO-processing signal 15003A is s1 (1),−s2*(1),s1 (2), −s2*(2), s1(3), −s2*(3), . . . , s1(i), −s2*(i), . . . , andpost-MISO-processing signal 15003B is s2(1), s1*(1), s2(2), s1*(2),s2(3), s1*(3), . . . , s2(i), s1*(i), . . . .

At this point, post-MISO-processing signals 15003A and 15003B correspondto post-processing baseband signals 12502A and 12502B in FIG. 125 ,respectively. The space-time block coding method is not limited to theabove method.

<Processing of Receiver>

In the transmission method, the modulation is performed based on thecode length N and modulation schemes α and β, which are assigned bycontrol signal 512. Accordingly, when recognizing code length N andmodulation schemes α and β, the receiver can demodulate the modulatedsignal modulated by the transmission method.

For example, information identifying code length N and modulationschemes α and β is transmitted from the transmitter as controlinformation symbols 12602, 12605A, and 1605B in FIG. 126 . For example,control information symbols 12602, 12605A, and 1605B are demodulated(and error-correction-decoded) with control signal demodulator 12401 ofthe receiver in FIG. 127 , and output as control information signal12402.

Signal processor 12705 determines code length N and modulation schemes αand β from control information signal 12402, and demodulates quadraturebaseband signals 12704X and 12704Y, which are obtained by receiving themodulated signals modulated by the transmission method, based ondetermined code length N and modulation schemes α and β.

For example, it is assumed that <Case 1>, in which the modulated signalis generated by the transmission method in FIG. 135 in the case thatcode length N has the 64800 bits while the set of modulation schemes αand β is the set of 64QAM and 256QAM, is previously decided between thetransmitter and the receiver.

Signal processor 12705 recognizes that 64764 bits in the 64800-bit codeword of the received signal are modulated by the set of 64QAM and 256QAMwhile the remaining 36 bits are modulated by the set of 64QAM and 64QAMfrom the information indicating code length N of 64800 bits, modulationscheme α of 64QAM, and modulation scheme β of 256QAM, the informationbeing determined from control information signal 12402.

Therefore, signal processor 12705 obtained 64764-bit log-likelihoodratio by demodulating quadrature baseband signals 12704X and 12704Y ofthe total of 4626 sets from set #1 to set #4626 using the demodulationscheme corresponding to the modulation scheme set of 64QAM and 256QAM.Signal processor 12705 also obtained 36-bit log-likelihood ratio bydemodulating quadrature baseband signals 12704X and 12704Y of the totalof 3 sets from set $1 to set $3 using the demodulation schemecorresponding to the modulation scheme set of 64QAM and 64QAM.

signal processor 12705 outputs the obtained (64764+36=64800)-bitlog-likelihood ratio as log-likelihood ratio signal 12706 (sometimessignal processor 12705 performs the deinterleaving processing).

Log-likelihood ratio signal 12706 and control information signal 12402are input to decoder 12707, and decoder 12707 performs the errorcorrection decoding from the error correction coding scheme included inthe control information, and outputs received data 12708.

The transmission method in FIG. 135 is described above by way ofexample. However, the demodulation and the decoding can be performed bynot only the transmission method in FIG. 135 but also any one of thetransmission methods of the exemplary embodiments.

When the transmitter transmits the control information indicating whichone of the transmission methods of the exemplary embodiments is used totransmit the signal, the receiver can recognize the transmission methodused in the transmitter from the control information, and obtain thedata. Accordingly, the control information transmitting method is notlimited to the above exemplary embodiments.

Summary of Exemplary Embodiments

According to a first aspect of the present disclosure, a transmissionmethod includes: performing error correction coding on an informationbit string to generate a code word having a number of bits that isgreater than a predetermined integral multiple of (X+Y); modulating afirst bit string in which the number of bits is the predeterminedintegral multiple of (X+Y) in the code word using a first scheme, thefirst scheme being a set of a modulation scheme in which mapping anX-bit bit string to generate a first complex signal and a modulationscheme in which mapping a Y-bit bit string to generate a second complexsignal; and modulating a second bit string in which the first bit stringis removed from the code word using a second scheme different from thefirst scheme.

According to a second aspect of the present disclosure, in thetransmission method of the first aspect, the second scheme is a set of amodulation scheme in which an A-bit bit string is mapped to generate athird complex signal and a modulation scheme in which a B-bit bit stringis mapped to generate a fourth complex signal, and

(A+B) is a divisor of the number of bits of the second bit string.

According to a third aspect of the present disclosure, in thetransmission method of the second aspect, further includes: transmittingcomplex signals generated by performing space-time block coding to thefirst complex signal and the second complex signal.

According to a fourth aspect of the present disclosure, in thetransmission method of the second aspect, the second scheme is a schemewhich generates a single-stream complex signal by using the thirdcomplex signal and the fourth complex signal.

According to a fifth aspect of the present disclosure, in thetransmission method of the fourth aspect, further includes: transmittingcomplex signals of a plurality of streams generated by performing thespace-time block coding, the complex signals of a plurality of streamsbeing generated by using the first scheme, and the single-stream complexsignal generated by not performing the space-time block coding, thesingle-stream complex signal being generated by using the second scheme.

According to a sixth aspect of the present disclosure, a transmitterincludes: an encoder that performs error correction coding on aninformation bit string to generate a code word having a number of bitsthat is greater than a predetermined integral multiple of (X+Y); and amapper that modulates a first bit string in which the number of bits isthe predetermined integral multiple of (X+Y) in the code word using afirst scheme, the first scheme being a set of a modulation scheme inwhich mapping an X-bit bit string to generate a first complex signal anda modulation scheme in which mapping a Y-bit bit string to generate asecond complex signal, and modulates a second bit string in which thefirst bit string is removed from the code word using a second schemedifferent from the first scheme.

According to a seventh aspect of the present disclosure, a receptionmethod includes: demodulating a received signal to generate ademodulated signal according to a first scheme and a second scheme; thefirst scheme being a scheme of a set of a modulation scheme in which anX-bit bit string is mapped to generate a first complex signal and amodulation scheme in which a Y-bit bit string is mapped to generate asecond complex signal, the second scheme being different from the firstscheme, the received signal being a signal obtained by receiving atransmitted signal transmitted from a transmitter, the transmittedsignal including a first signal and a second signal, the first signalbeing generated from a first bit string that is of a predeterminedintegral multiple of (X+Y) using the first scheme, the second signalbeing generated from the second bit string in which a number of bits isnot the predetermined integral multiple of (X+Y) using the secondscheme, a code word constructed with the first bit string and the secondbit string being generated by performing error correction coding oninformation bit string; and performing error correction decoding on thedemodulated signal.

According to an eighth aspect of the present disclosure, a receiverincludes: a signal processor that demodulates a received signal togenerate a demodulated signal according to a first scheme and a secondscheme, the first scheme being a scheme of a set of a modulation schemein which an X-bit bit string is mapped to generate a first complexsignal and a modulation scheme in which a Y-bit bit string is mapped togenerate a second complex signal, the second scheme being different fromthe first scheme, the received signal being a signal obtained byreceiving a transmitted signal transmitted from a transmitter, thetransmitted signal including a first signal and a second signal, thefirst signal being generated from a first bit string that is of apredetermined integral multiple of (X+Y) using the first scheme, thesecond signal being generated from the second bit string in which anumber of bits is not the predetermined integral multiple of (X+Y) usingthe second scheme, a code word constructed with the first bit string andthe second bit string being generated by performing error correctioncoding on information bit string; and a decoder that performs errorcorrection decoding on the demodulated signal.

While the exemplary embodiments are described above with reference tothe drawings, the present disclosure is not limited to the exemplaryembodiments. It will be obvious to those skilled in the art that variouschanges and variations can be made within the appended claims, and itshould be understood that these changes and variations fall within thetechnical scope of the present disclosure. The constituents of theexemplary embodiments may arbitrarily be combined without departing fromthe scope of the present disclosure.

INDUSTRIAL APPLICABILITY

The present disclosure can widely applied to a radio system thattransmits different modulated signals from the plurality of antennas.The present disclosure can also applied to the case that the MIMOtransmission is performed in wired communication system (such as a PLC(Power Line Communication) system, an optical communication system, anda DSL (Digital Subscriber Line) system) including the plurality oftransmission points.

REFERENCE MARKS IN THE DRAWINGS

-   -   502,502LA encoder    -   502BI bit interleaver    -   5701,6001,7301,8001 bit length adjuster    -   504 mapper

What is claimed is:
 1. A transmission method comprising: encoding, withan encoder, first information according to a first coding rate and afirst coding length to generate a first encoded data sequence, the firstcoding length being 16200; encoding, with the encoder, secondinformation according to the first coding rate and a second codinglength to generate a second encoded data sequence, the second codinglength being 64800; generating an appended data sequence from the firstencoded data sequence by appending a part of the first encoded datasequence; mapping, with a mapper, the appended data sequence onto 64signal points defined by a first 64 Quadrature Amplitude Modulation(QAM) scheme to generate a first modulation symbol sequence; mapping,with the mapper, the second encoded data sequence onto 64 signal pointsdefined by a second 64 QAM scheme to generate a second modulation symbolsequence; transmitting a signal generated based on the first modulationsymbol sequence and the second modulation symbol sequence, wherein the64 signal points are representable on an I-Q plane having a real axisand an imaginary axis such that a distance between adjacent signalpoints has nonuniformity, the 64 signal points defined by the first 64QAM scheme have a first arrangement pattern on the I-Q plane, and the 64signal points defined by the second 64 QAM scheme have a secondarrangement pattern on the I-Q plane different from the firstarrangement pattern.